This is one of the most important parts of this course – I want you to work with your group to design a follow-up study using conformity / consensus. As you work on this discussion, try to think about what other variable might influence participant impressions. Let me give you a few example, though try to get creative with your group. Look at prior research and see if you can use some of their work as a follow-up to your study. Have fun with it!

First, you can alter the gender of the Facebook user. What if you are looking at Adam rather than Abigail? Would support (versus mixed) for Adam get different ratings compared to support (versus mixed) for Abigail? (Note that we would have FOUR conditions in this design: Adam Support vs. Adam Mixed vs. Abigail Support vs. Abigail Mixed).
Second, source credibility is a good topic to explore. Have some participants in the support condition and others in the mixed condition. Then, some participants are told the cheater user is a high-school student (which might imply youth and inexperience) while others are told the cheater is a college student (which might imply age and wisdom).

In this discussion, I want EACH of you to do three things.

First, tell me which study you want to do (that is, which second independent variable you find most interesting).

Second, give me a reference in APA format for one peer reviewed research article that has something to do with this second variable. This article does not have to involve conformity / consensus at all, but it must have something to do with your second independent variable.

Third, give me a hypothesis for what you expect to occur if your new independent variable is chosen for the class project.  

Lab Presentation
Week 7 Lab
Generating an Idea for Study Two

Overview of The Lab
This week during the lab, we are going to focus on your Study Two (a follow-up to Study One that takes the Facebook Consensus study one step further).
In this presentation, we will discuss the following:
Part One: The Papers to Come (Papers III, IV, and V)
Part Two: Generating a Study Two Idea
Part Three: Your Task This Week
Part Four: An Eye Toward The Future

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Part One
The Papers to Come: Papers III, IV, and V

The Papers to Come: Papers III, IV, & V
This week during the lab, we have a big project: Thinking about study two
Before we get to that idea, let me give you more information about Papers III, IV, and V …

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The Papers to Come: Papers III, IV, & V
Paper III: Literature Review (Study Two)
Paper III is your second chance to write a literature review.
Once again, you will use your Facebook Consensus Study as a starting point, writing an APA formatted introduction to your second study that sums up how prior research led to your research hypotheses
Paper III should be easy, as it is simply an extension of Papers I and II! That is, you know the basic process of starting broad and narrowing your paper down to your hypothesis (using APA formatting along the way, of course!)

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The Papers to Come: Papers III, IV, & V
Paper III: Literature Review (Study Two)
So how does Paper III differ from Paper I?
Essentially, Paper III combines the title page and literature review from your Paper I with the methods, results, and brief discussion from your Paper II into one longer paper.
Paper III then adds a second “literature” review (after the brief Paper II discussion) based on an extension study (study two). This new study two literature review highlights a second IV of interest to you and your classmates. Paper III focuses on both your new IV and your old IV to see how they might interact

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The Papers to Come: Papers III, IV, & V
Paper III: Literature Review (Study Two)
So how does Paper III differ from Paper I?
Consider study one. We used three levels of Facebook feedback. In study two, we will drop one of those levels (we will retain either the Support vs. Oppose conditions only, OR we will retain the Support vs. Mixed only)
We will then add a second IV that has two levels.
I’ll talk more about that in a few slides.
For now, think about Paper III as a continuation of Papers I and II

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The Papers to Come: Papers III, IV, & V
Paper IV: Methods and Results (Study Two)
Paper IV is very similar to Paper II. You will write a Methods, Results and brief discussion section, but this time for a factorial research design (a 2 X 2 study)
IMPORTANT: Paper IV is not a simple repeat of Paper II. It has a new methods and results section using a new study design. If you simply copy and paste your Paper II results into this paper, you will NOT receive credit for Paper IV.

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The Papers to Come: Papers III, IV, & V
Paper V: The Final Paper (Study Two)
Paper V is your final paper. This will be fairly easy, as it will combine Papers I, II, III and IV into one cohesive paper, with:
Your title page
An abstract (brand new for the final paper)
Study one literature review, methods, results, discussion
Study two literature review, methods, results, discussion
General discussion (brand new for the final paper)
References
SPSS tables (copied from SPSS output)

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The Papers to Come: Papers III, IV, & V
Paper V: The Final Paper (Study Two)
The final paper thus incorporates everything you will have learned in the course, focusing once again on the concept of Facebook Consensus. You have a lot of time to work on these papers, so we will go at a nice steady pace.
The only thing to figure out now is where to go with this topic as we create Study Two …

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Test Your Understanding
How many conditions will your study two have?
A. One
B. Two
C. Three
D. Four
E. None of the above

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Test Your Understanding
How many conditions will your study two have?
A. One
B. Two
C. Three
D. Four
E. None of the above
Your study two uses a 2 X 2 design. That is, we will have two independent variables, each with two levels. This will create four different conditions (all independently / randomly assigned)

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Part Two
Generating a Study Two Idea

Generating a Study Two Idea
For the rest of this lab, we are going to discuss the following:
1). Study Two Topic
2). Study Two Guidelines
3). Your Task This Week
4). An Eye Toward the Future

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Generating a Study Two Idea
1). Study Two Topic
For Study Two, I want you to use a factorial study design. That is, rather than just one independent variable with three levels, this new study will have two independent variables, each of which have two levels (a 2 X 2 study with four conditions total).
Thus, for this final study, I want you to do a follow-up study on the Consensus topic using a second independent variable

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Generating a Study Two Idea
1). Study Two Topic
I want to repeat that again, because it is VERY important
For your final study, you will design a factorial study (more than one IV) to expand on your Facebook Consensus study
For this second study, use your first study as a starting point. That is, use S vs. M as one IV and then add a second IV. Or you can look at O vs. M. It’s your lab’s choice (and all members must agree), but I highly recommend S versus M
This week, I want each of YOU to propose some potential new study ideas and come up with potential hypotheses for your follow-up study

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Generating a Study Two Idea
1). Study Two Topic
Keep in mind some constraints that we have for Study Two
You are going to collect data for study two (just as you did in study one), but we are going to collect data online this time using an internet survey program called “Qualtrics”
In a few weeks, you and your instructor will post materials on Qualtrics and you will personally recruit at least 5 people to participate on your behalf. First, though, we need to develop your independent variables and your hypotheses

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Study Two Guidelines
2). Study Two Guidelines
Using Qualtrics, we will randomly assign our participants to one of four different conditions, creating a true experimental design
For Study Two, we are going to develop a 2 X 2 design
This means we have two independent variables, and each IV has two levels (I know I’m being repetitive – it’s important)
Just as a comparison, a 2 X 3 design has two IV’s, one of which has 2 levels and one that has 3 levels
A 2 X 2 X 3 design has three IV’s, one with 2 levels, another with 2 levels, and the last with 3 levels

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Study Two Guidelines
2). Study Two Guidelines
I’ve been thinking about the following set-up on the next few slides myself, but this is just one possibility. Your class can go in a completely different direction if you want (and I encourage your creativity! The info below is just a suggestion)
We can present participants with a multipage internet survey and then have them complete questions at the end.
Each page presents them with either IVs or DVs
You’ve probably done online studies yourself already. Well, imagine this set-up for an online study that you control …

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Study Two Guidelines
2). Study Two Guidelines
A. Page one: Informed consent page
B. Page two: IV page
C. Page three: DV page
D. Page four: Demographics page
E. Page five: Debriefing form

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Study Two Guidelines
2). Study Two Guidelines
A. Page one is easy. We have to create an informed consent page. We will get to this document in the lab next week.
For now, let’s look at page two …

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Recall your Facebook Consensus topic from study one. In study two, we can manipulate the survey in a similar way
Page two is where you have input. In this “priming” page, we expose some participants to one level of our IV and the rest of the participants to the other level of the IV

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Recall your Facebook Consensus topic from study one. In study two, we can manipulate the survey in a similar way
First, we could keep it as is. Some look at Support; some look at Mixed
Note: Why not look at the Oppose condition? Our study is about consensus, so we need one condition that has consensus and one that does not. It is thus important to drop a consensus condition. Here, I think the Support consensus is more useful than Oppose

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Recall your Facebook Consensus topic from study one. In study two, we can manipulate the survey in a similar way
Second, we could manipulate consensus differently
Rather than listing eight supportive comments, we could have ONE person say all of his friends thought cheating was ok (vs. “most” friends said it was ok)
Or we could provide a percentage. That is, we could tell our participants that 100% of prior participants said cheating was ok (vs. 20% said it was ok).

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Recall your Facebook Consensus topic from study one. In study two, we can manipulate the survey in a similar way
My advice, though, is to keep the original comments. That way you have a better connection between Study One and Study Two, allowing you to draw much better comparisons between the two studies in your final paper

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
First, recall that measured IVs get at characteristics the participants bring with them to the laboratory.
This can involve demographics (e.g. do men respond differently than women?) or attitudes (e.g. do people high in need for consistency respond differently than those low in need for consistency?).
Or what if we determined if participants also cheated

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
First, recall that measured IVs get at characteristics the participants bring with them to the laboratory.
Remember that with measured variables, you cannot draw causal conclusions (we cannot assign someone to an attitude or a demographic characteristic).
For our second study, a measured variables might be based on participant locus of control …

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
First, recall that measured IVs get at characteristics the participants bring with them to the laboratory.
An internal locus of control focuses on a person believing they are responsible for an outcome; an external locus of control focuses on outside factors being responsible. Would internal LOC p’s feel like cheating was okay versus not okay?

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
For example, we could see if forewarning people about the effects of consensus influences their ratings of cheating. That is …
Idea #1

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
… we could tell some participants about the idea of consensus before they see the Facebook posts to see if the warning impacts their DV ratings. Others would not get this warning. Thus …
Idea #1

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
… some participants would get support + a warning, some get mixed + a warning, some get support + no warning, and the rest mixed + no warning.
Four conditions total in this 2 X 2 design!
Idea #1

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
Or, we could alter the gender of the Facebook user. What if we have Abigail (female) vs. Albert (male)? Would the user’s gender interact with the support versus mixed comments? (support + male, support + female, mixed + male, mixed + female)
Idea #2

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
Or, what if Abigail was young for some participants (new college student, early twenties) versus an older student (forties) for others?
Or, what if Abigail is Caucasian in some conditions but African American or Hispanic in others?
Idea #3

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
Or what if Abigail’s posts received a lot of “likes” for the support (vs. mixed) posts versus very few “likes”
Or what if we used different emojies (like response, love response, angry face response, laughing face response, angry face response, etc.)
Idea #4

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
Or we could alter the type or number of “comments”. Since this is an online study, we could do more than eight comments back. So what if one condition has 20 supportive comments; one has 8 supportive; one has 20 mixed comments; one has 8 mixed?
Idea #5

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
What if we look at different “moral” situations? We can keep the test-cheating Abigail post for some participants (with both support and mixed comments for conditions 1 and 2), but add in a new morality situation for conditions 3 and 4 …
Idea #6

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
That is, in conditions 3 and 4, Abigail admits that she saw a woman drop a gift card outside a store for $100. The woman drove off before Abigail could say anything, so rather than alerting the store, she kept the gift card and wants to know if it was bad …
Idea #6

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
For this Idea #6, would participants see the behavior as more immoral if it involved a test-cheating situation or if it involved not telling anyone about found money?
Idea #6

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
My final idea is to see if participants alter their views depending on whether they are asked to think about Abigail’s cheating emotionally (versus rationally).
We could even have participants write about an emotional (versus rational) experience to prime them
Idea #7

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Now let’s talk about your second IV. This second variable is more flexible, and can be either manipulated or measured
Second, I usually prefer manipulated IVs. Here, we alter something else (in addition to our S and M groups)
I gave you a bunch of possible studies, but PLEASE feel free to come up with your own idea, as there are THOUSANDS of other possibilities. Use your lit review experience as a jumping off point. Just remember that our class will choose ONE of them.

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Test Your Understanding
Why is it important to reuse at least some material (either IV or DV related) from study one when we engage in study two?
A. We want to see if we can replicate some study one results
B. We want to extend study one to see how a new independent variable interacts with the original independent variable
C. We want to be able to draw good comparisons between study one and study two in our eventual final paper
D. All of the above

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Test Your Understanding
Why is it important to reuse at least some material (either IV or DV related) from study one when we engage in study two?
A. We want to see if we can replicate some study one results
B. We want to extend study one to see how a new independent variable interacts with the original independent variable
C. We want to be able to draw good comparisons between study one and study two in our eventual final paper
D. All of the above
Easy one here – all of these elements are important

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Study Two Guidelines
2). Study Two Guidelines
B. Page two: First IV page (2 versions)
Please be creative with your IVs. Don’t feel restricted to the design we used for study one (though feel free to replicate it if you really want!). If you do go in a different direction, note that your DVs are going to differ as well. At minimum, we need two independent variables, so keep that in mind!
C. Okay, let’s move on and look at page three and some of those new DVs…

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Study Two Guidelines
2). Study Two Guidelines
C. Page three: DVs page
The third page of your new study should ask about your dependent variables. Make sure to measure responses that are pertinent to your study design
You can use as many of the variables from study one as you want or you can have different variables. Just recall that you want to have connections between study one and study two, so the more they overlap the better you can compare and contrast them in Paper V later this semester (e.g. “Study two findings replicated study one”)

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Study Two Guidelines
2). Study Two Guidelines
D. Page four: Demographics page
Page four will be easy. You can reuse the demographics set-up from Study One (though add potential new factors if you find them important. For example, if you do a religious based second independent variable, you might want to ask for the participant’s religion)
Demographics can come at either the start of the study or the end: put them where you think they work best

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Study Two Guidelines
2). Study Two Guidelines
E. Page five: Debriefing Statement
Page five is also easy. You’ll need to tell your participants what you did, why you did it, and what you predict.
Of course, you’ll need to have your study idea and its hypothesis in mind, which brings us to your next task for this lab session …

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Part Three
Your Task This Week

Your Task This Week
3). Your task this week
Note: For a 2 X 2 study, we will have a more complex set of hypotheses. For each dependent variable we will actually have three types of hypotheses. This includes two main effects and one interaction for each dependent variable
A main effect looks at the impact of one IV regardless of the presence of the other IV
An interaction looks at the simultaneous impact of both IVs working in concert on the DV

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Your Task This Week
3). Your task this week
Note: For a 2 X 2 study, we will have a more complex set of hypotheses. For each dependent variable we will actually have three types of hypotheses. This includes two main effects and one interaction for each dependent variable
For now, imagine we create a 2 X 2 study where one IV is consensus (support vs mixed) and a second is manipulated warning (warn about consensus vs do not warn).
This gives us four study conditions: Support + Warning, Support + No Warning, Oppose + Warning, Oppose + No Warning

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Your Task This Week
3). Your task this week
Note: For a 2 X 2 study, we will have a more complex set of hypotheses. For each dependent variable we will actually have three types of hypotheses. This includes two main effects and one interaction for each dependent variable
So, imagine we have consensus as IV #1 (support v. mixed) and warning as IV #2 (warned v. not warned)
Let’s see look at main effect and interaction hypotheses …

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Your Task This Week
3). Your task this week
2 X 2 study: Main Effects
Consider a 2 (Condition: Support vs. Mixed) X 2 (Warning: Warned vs. Not Warned) study
Condition and Warning are our two IVs (2 X 2)
Consider “Abigail’s behavior was wrong” as our DV
Main effect #1: Looking only at condition, I expect a main effect for condition, with support participants feeling the cheating was less wrong than mixed participants
Note: this ONLY looks at condition, NOT self-esteem
#1

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Your Task This Week
3). Your task this week
2 X 2 study: Main Effects
Consider a 2 (Condition: Support vs. Mixed) X 2 (Warning: Warned vs. Not Warned) study
Condition and Warning are our two IVs (2 X 2)
Consider “Abigail’s behavior was wrong” as our DV
Main effect #2: Looking only at warning, I don’t expect there to be a significant impact of warning all on its own (it needs the other IV to impact participants).
Still, this looks ONLY at warning, NOT condition
#2

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Your Task This Week
3). Your task this week
2 X 2 study: Interactions
Consider a 2 (Condition: Support vs. Mixed) X 2 (Warning: Warned vs. Not Warned) study
Condition and Warning are our two IVs (2 X 2)
Consider “Abigail’s behavior was wrong” as our DV
Interaction: Here, participants should rate the behavior as less wrong in the support + no warning condition and most wrong in the mixed + warning condition. The other two conditions (support + warning and mixed + no warning) will fall in between these extremes
Int

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Your Task This Week
3). Your task this week
2 X 2 study: Main effects and Interactions
So keep in mind that each DV we look at may have three hypotheses (2 main effects and 1 interaction).
We could go back and look at other DVs as well.
“Abigail’s behavior was unacceptable”
“I would advise Abigail to keep silent”
“Abigail seems warm” etc.
Okay, time for your assignment. Come up with a 2 X 2 study design idea and share it with your classmates!

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Your Task This Week
3). Your task this week
As soon as your lab instructor sees all of your wonderful ideas, he or she will pick out the ones that seem most interesting and let the class choose which one to pursue.
Sorry, we will only do one idea for the whole class this semester. Well … actually, we will do one study across all online sections, so this will go beyond just your specific online class as well.
Sorry again! You can concentrate on more individualized studies in your future psychological career!

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Test Your Understanding
How many main effects and interactions will we look at in a 2 X 2 study design?
A. One main effect and one interaction
B. One main effect and two interactions
C. Two main effects and one interaction
D. Two main effects and two interactions

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Test Your Understanding
How many main effects and interactions will we look at in a 2 X 2 study design?
A. One main effect and one interaction
B. One main effect and two interactions
C. Two main effects and one interaction
D. Two main effects and two interactions
Consider independent variables A and B. We will have one main effect for variable A, one main effect for variable B, and one interaction of variables A and B

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Part Two
An Eye to the Future

An Eye To The Future
Study Two Materials
Don’t worry about your materials for your new study this week, but start thinking about some of the materials you will need for your study
Next week, once we have established your 2 X 2 design for the study, you will start working on your materials (informed consent, IV 1, IV 2, DVs, demographics, debriefing form)
We have a few weeks to work on this, as the materials won’t be due for some time, but start thinking ahead while you build your research hypothesis!

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An Eye To The Future
Other assignments
Keep in mind that your Paper II: Study One Methods, Results, and Discussion will be due soon. Instructions and guidelines for that paper (as well as an example paper) are available on Canvas

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Chapter 17 (Salkind)
What To Do When You’re Not Normal

Overview of this Chapter
The Good News and the Bad News
First up, the Bad News. Once again, we will look at statistics. Here, that means the Chi Square, a type of statistics we rely on when our scales are nominal or ordinal
The other Bad News is that this there are formulas and tables associated with this chapter. I know, ugh
The Good News? Some of this might be a review! But you will need some of the new information here as you work on one statistical calculation for your research paper: The Chi Square

Overview of this Chapter
In this chapter, we will focus on …
Part One: Introduction To Non-Parametric Statistics
Part Two (A): Introduction To The One-Sample Chi-Square
Part Two (B): Chi Square Test Of Independence
Part Three: Computing The Chi-Square Statistic
Part Four: Using The Computer To Perform A Chi-Square Test
Part Five: Other Non-Parametric Tests You Should Know
Part Six: An Eye Toward The Future

Part One
Introduction To Non-Parametric Statistics

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
Last semester in Research Methods and Design One (and last week in Chapter 9, Smith and Davis), we talked about normal curves and why we need normality in order to run ANOVAs, t-Tests, and other “parametric” tests.
“Parametric tests” infer that the results obtained from a sample in the study easily applies to a population from which that sample was drawn. But such “normal” tests are based on a series of assumptions …

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
Four parametric test assumptions:
Assumption #1: Variances in each group are homogenous (that is, the two or more groups are similar in variability)
Assumption #2: The sample is large enough to adequately represent the population (e.g. it isn’t a biased sample)

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
Four parametric test assumptions:
Assumption #3: The statistical test uses interval or ratio scales of measurement (the I and R in NOIR)
Assumption #4: The characteristic under consideration is normally distributed (i.e. has a normal curve)

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
So what happens when/if a test violates these assumptions?
In some cases, t-Tests, ANOVAs, and other parametric tests are robust (e.g. strong enough) that the assumptions can be violated without too much hassle.

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
So what happens when/if a test violates these assumptions?
Non-parametric tests may be used when assumptions are violated
“Non-parametric” statistics are essentially distribution-free, meaning they don’t follow the same rules as the parametric tests
They don’t require homogeneity of variance and they can examine more than just interval and ratio data

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
So what happens when/if a test violates these assumptions?
Researchers often use non-parametric statistics used when the data set relies on frequencies or percentages (rather than scales), and we can test whether the percentages we see in a data set are what we would expect by chance alone
This takes us to one of the more common non-parametric tests, the chi square (something you’ll use for your first study this semester!)

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
Before we get too far into this chapter, I just want you to think about the concept of “expectations”
Let’s say I go to a pet store to look at kittens, and there are dozens of them. Just looking at them from afar, what percent would you expect to be female?
About a 50 / 50 chance, right? Although we might “expect” this, we might be wrong. Chi Squares can help us see if our expectations match reality!

Pop Quiz – Quiz Yourself
If you have 30 respondents identifying their political preference (i.e., Democrat, Republican, Independent), how many of each political affiliation would you expect?
A). 10
B). 20
C). 30
D). 40

Pop Quiz – Quiz Yourself
If you have 30 respondents identifying their political preference (i.e., Democrat, Republican, Independent), how many of each political affiliation would you expect?
A). 10
B). 20
C). 30
D). 40
Maybe, right? We SHOULD get 10 of each, but in reality there tend to be very few Independents (voters usually fall into either Democrat or Republican camps, so “10” might be too high for Independents!)

Introduction – Non-Parametric Statistics
Introduction To Non-Parametric Statistics
In the next part of this presentation, I want to tell you about two different types of chi squares we can run. We will split them up into two “flavors”:
Part Two (Section A): The One-Sample Chi Square
This one is more FYI (though you will be tested on it!
Part Two (Section B): Chi Square Test of Independence
This one is very important for your Paper II analysis!
We’ll figure out how to compute each when we start Part Three

Part Two (Section A)
Introduction To The One-Sample Chi-Square

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
The one sample chi-square is a non-parametric test that allows you to determine if what you observe in a frequency distribution of scores is what you would expect by chance, though this is limited to a single sample

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
The one sample chi-square is a non-parametric test that allows you to determine if what you observe in a frequency distribution of scores is what you would expect by chance, though this is limited to a single sample
Consider ”year in college” as our “one sample” for students at FIU. For expectations, we ask, “What percent represents Freshmen, Sophomores, Juniors, and Seniors?” We can then compare our “expectations” to our “observations.”

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
We would probably expect a few more Freshmen than other groups, right? After all, not all Freshmen will return for their senior year, and not all Sophomores return as Juniors, etc.
But generally, let’s say we expect around 25% of each class each year. If we look at the actual observations, would they be higher or lower than what we would “expect” by chance?

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
That’s a question we can answer using the chi square
At FIU, our total enrollment is around 50,000
So we might expect around 12,500 Freshmen (or one fourth of the total enrollment)? What if we found 15,000 Freshmen? Would that be outside the realm of expectation?
FIU has a retention rate of 84% of Freshmen (84% of Freshmen return as Sophomores), which is high but still shows that some students are not “retained”

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
That’s a question we can answer using the chi square
The chi square tests the actual occurrences against the expected occurrences to see if they differ significantly
This means that if there is no difference between what we observe and what we would expect by chance, our chi square will be close to zero

Pop Quiz – Quiz Yourself
If you have 100 respondents identify their region of residence (i.e., north, south, east, or west), what would the expected frequency be for each category?
A). 33
B). 50
C). 25
D). 100

Pop Quiz – Quiz Yourself
If you have 100 respondents identify their region of residence (i.e., north, south, east, or west), what would the expected frequency be for each category?
A). 33
B). 50
C). 25
D). 100
But again, expectation and reality may differ a lot!

Introduction: One-Sample Chi-Square
Introduction To One-Sample Chi-Square
What is the one-sample chi-square all about?
As you can see, the one-sample chi square focuses on just one variable, or one sample
Here, we looked at the number of students who fall into each year (Freshmen, Sophomore, Junior, or Senior)
But what if we want to look at more than one variable? Well, that calls for a chi square test of independence …

Part Two (Section B)
The Chi-Square Test Of Independence

The Chi-Square Test Of Independence
The Chi Square Test Of Independence
As you just saw, we can see if the observed counts of a single variable match (or do not match) the counts we would expect by chance
Often, though, you will also want to see if the observed counts across two variables match (or mismatch) the counts we would expect by chance. In this situation, you use a chi square test of independence (two samples)

The Chi-Square Test Of Independence
The Chi Square Test Of Independence
Go back to our Freshmen, Sophomore, Junior, and Seniors at FIU. Do you think there is a difference in terms of percentages of students in each year?
We could answer this using a one-sample chi square
But do you think there might also be a difference for each of these classes between male and female students?
This question deals with two samples (year and gender), so we must answer it using a chi square test of independence

The Chi-Square Test Of Independence
The Chi Square Test Of Independence
Given four “years” (Freshmen, Sophomore, Junior, and Senior) and two “genders” (Male and Female), we might expect 12.5% of students to fall into each of our eight table cells:

Will our “observations” match our “expectations”? Let’s find out
Gender Year in College
Freshman Sophomore Junior Senior
Male 12.5% 12.5% 12.5% 12.5%
Female 12.5% 12.5% 12.5% 12.5%

Pop Quiz – Quiz Yourself
A two-sample chi-square is also known as a ________.
A). Goodness of fit test
B). Test of independence
C). Wilcoxon rank
D). Mann-Whitney U

Pop Quiz – Quiz Yourself
A two-sample chi-square is also known as a ________.
A). Goodness of fit test
B). Test of independence
C). Wilcoxon rank
D). Mann-Whitney U

Part Three
Computing The Chi-Square Test Statistic

Computing The Chi-Square Test Statistic
Let’s focus on each test separately
1). Computing the one sample chi square test statistic
2). Computing the chi square of independence test statistic

Computing The Chi-Square Test Statistic
1). Computing The One Sample Chi-Square Test Statistic
The one sample chi square test compares what we observe with what we expect by chance. It uses this formula

X2 is the chi-square value
Σ is the summation sign
O Is the observed frequency
E is the expected frequency
X2 = Σ
(O – E )2
E

Computing The Chi-Square Test Statistic
1). Computing The One Sample Chi-Square Test Stastic
Let’s say we get the following data from our enrollment rosters at FIU (including all online, live, MMC, and BBC students!)

Time to walk through out eight research steps! I trust you recall all of these from Research Methods and Design One!
Freshmen Sophomores Juniors Seniors Total
15,000 13,500 11,000 10,500 50,000

Computing The Chi-Square Test Statistic
1). Computing The One Sample Chi-Square Test Statistic
Step One: State the null and alternative research hypotheses
Our null hypothesis is that the four groups do not differ
HO: PFresh = PSoph = PJunior = PSenior
Our research (alternative) hypothesis is there are differences in the proportion of occurrences in each “year” category
H1: PFresh ≠ PSoph ≠ PJunior ≠ PSenior

Computing The Chi-Square Test Statistic
1). Computing The One Sample Chi-Square Test Statistic
Step Two: State the level of risk
Similar to last semester, we get to set our own risk. We’ll go with the usual psychology suspects, either p < .05 or p < .01 Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Three: Select the appropriate test statistic We are looking at categories for our one sample data set, or Freshmen, Sophomores, Juniors, and Seniors As such, we are dealing with a nominal variable, right! We need to use the mean if we want to run parametric tests like a t-Test or an ANOVA, but since we have a nominal variable, the mean is … meaningless here What would our mean even be? Something between a Freshman and a Sophomore. What is that, some kind of Freshomore? Makes no sense! Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Three: Select the appropriate test statistic We are looking at categories for our one sample data set, or Freshmen, Sophomores, Juniors, and Seniors Given our nominal “year” variable, we have to use a non-parametric test here. The chi-square is perfect, as it can examine categorical (nominal) variables Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Consider our “year” data again (Note: I did make these up!) To set up our chi-square calculations, we need to look at the observed frequency (tabled above), our expected frequency (there are four groups, so divide 50,000 by 4 to get 12,500 each). We need the difference, too, and some squaring! … Freshmen Sophomores Juniors Seniors Total 15,000 13,500 11,000 10,500 50,000 Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Here are our observed and expected values Year Observe Expect Difference (O – E)2 (O – E)2 / E Fresh. 15000 12500 Soph. 13500 12500 Junior 11000 12500 Senior 10500 12500 Total Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Subtract observed from the expected (ignore negative signs) Year Observe Expect Difference (O – E)2 (O – E)2 / E Fresh. 15000 12500 2500 Soph. 13500 12500 1000 Junior 11000 12500 1500 Senior 10500 12500 2000 Total Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Square each difference number (e.g. 2500 X 2500 = 6250000) Year Observe Expect Difference (O – E)2 (O – E)2 / E Fresh. 15000 12500 2500 6250000 Soph. 13500 12500 1000 1000000 Junior 11000 12500 1500 2250000 Senior 10500 12500 2000 4000000 Total Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Divide the square of each difference by its “expected” number Year Observe Expect Difference (O – E)2 (O – E)2 / E Fresh. 15000 12500 2500 6250000 500 Soph. 13500 12500 1000 1000000 80 Junior 11000 12500 1500 2250000 180 Senior 10500 12500 2000 4000000 320 Total Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Four: Compute the test statistic Our total chi square value is 500 + 80 + 180 + 300 = 1080 Year Observe Expect Difference (O – E)2 (O – E)2 / E Fresh. 15000 12500 2500 6250000 500 Soph. 13500 12500 1000 1000000 80 Junior 11000 12500 1500 2250000 180 Senior 10500 12500 2000 4000000 320 Total 1080 Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Five: Determine the value needed to reject the null If you look in Appendix B (Salkind), you’ll see the chi-square table starting on page 380 But we must first determine our degrees of freedom. For the one sample chi square, this is r – 1, where r is the # of rows In this case, we have four rows (four “years”), so r – 1 gives us 4 – 1, or 3 for our degrees of freedom Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Five: Determine the value needed to reject the null Using df = 3, look up the critical value In this case, with a df of 3, we need to surpass a critical value of 7.82 for the p < .05 level and 11.34 to surpass the p < .01 level Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Six: Compare the obtained value and the critical value We compare our obtained value of 1080 to our critical value of 7.82 (for p < .05) and 11.34 (for p < .01) Is 1080 larger than either 7.82 or 11.34? Well … Computing The Chi-Square Test Statistic 1). Computing The One Sample Chi-Square Test Statistic Step Seven / Eight: Make a decision Since 1080 is clearly larger than our critical values, we can conclude that the null hypothesis cannot be accepted. Our observed values differ from our expected values The “goodness of fit” (another name for the chi-square test) is not very “good” here. That is, our observed data does not “fit” the expected data Computing The Chi-Square Test Statistic So How Do I Interpret X2(3) = 1080, p < .01 X2 represents the test statistic (Chi square) 3 is the number of degrees of freedom (r – 1, or 4 – 1 = 3) 1080 is the obtained value p < .01 indicates that the probability is less than 1% that the null hypothesis is correct across all categories by chance alone Computing The Chi-Square Test Statistic How Would I Write Up This Result In A Results Section? “A chi-square goodness-of-fit test was performed to determine whether FIU students were equally distributed across the four years in college. Results showed that the students were not equally distributed, X2(3) = 1080, p < .01.” Pop Quiz – Quiz Yourself If our degrees of freedom is 20, what critical value do we need to overcome to conclude that our obtained value is significant at the p < .01 level? A). 24.89 B). 31.41 C). 36.19 D). 37.57 E). 38.93 Pop Quiz – Quiz Yourself If our degrees of freedom is 20, what critical value do we need to overcome to conclude that our obtained value is significant at the p < .01 level? A). 24.89 B). 31.41 C). 36.19 D). 37.57 E). 38.93 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic We just looked at a one sample chi square, but sometimes we have more than one variable that we may want to assess, all of which are nominal in nature For example, what if we want to see if there is a difference in “year” based on “gender” of the student. We might get a table like this for our “expectations” for a population of 50,000 FIU students … Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Two group design This includes 50,000 students total, or 25,000 males and 25,000 females (if you do the 50/50 split for gender). Divide 25,000 by four years, and you get 6250 per year (12.5% of 50,000 gets us to this 6250 as well!). Nice and easy, right! Gender Freshmen Sophs. Juniors Seniors Males 6250 6250 6250 6250 Females 6250 6250 6250 6250 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Two group design Yeah, nothing is really easy in statistics. In fact, when you look at more than one variable, the simple “expectation” route is not really appropriate. In fact … Gender Freshmen Sophs. Juniors Seniors Males 6250 6250 6250 6250 Females 6250 6250 6250 6250 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Two group design FORGET the scores above! The chi-square of independence uses a statistical calculation of the expectation, which is based on the expected value for one variable working in concert with the expected value for the second variable. Ugh. Calculations: Gender Freshmen Sophs. Juniors Seniors Males 6250 6250 6250 6250 Females 6250 6250 6250 6250 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Two group design – The “Real Expected” values Do you want to know what the “Real Expected” values are? Well, here they are … Gender Freshmen Sophs. Juniors Seniors Males Females Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Two group design – The “Real Expected” values You’re probably scratching your head right now, wondering how I got these numbers. This is where some calculations come into play. Believe it or not, we need to begin with our “observed” values to calculate our “expected” values … Gender Freshmen Sophs. Juniors Seniors Males 6975 6277.5 5115 4882.5 Females 8025 7222.5 5885 5617.5 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Consider our “observed” values below, the values we actually observe. (Note: I made up the data below, but it is possible!) What we need now are totals for the columns and rows … Gender Freshmen Sophs. Juniors Seniors Males 7000 6000 5250 5000 Females 8000 7500 5750 5500 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Here’s a rearranged table that adds blank cells for each row (?) and each column (?) as well as a Column Total + Row Total (?) Let’s fill in the blank cells by doing some basic addition Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 ? Female 8000 7500 5750 5500 ? Column Total ? ? ? ? ? Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Pretty easy, right. Our male total is 7000 + 6000 + 5250 + 5000 = 23250 Freshmen total is 7000 + 8000 = 15000, and so forth Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Now multiply each row by each column and divide by total N, which will give us our expectation for each gender*year cell Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Freshman males, we have 15000*23250 / 50000 = 6975 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic That is, for Freshman males, our expected value is 6975! Thus we expect 6975 Freshman males. Let’s table that quickly … Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Here is our new “Expectation” (Mathematically Derived) Gender Freshmen Sophs. Juniors Seniors Males 6975 Females Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Soph. males, we have 13500*23250 / 50000 = 6277.5 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic Here is our new “Expectation” (Mathematically Derived) And so on … Gender Freshmen Sophs. Juniors Seniors Males 6975 6277.5 Females Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Junior males, we have 11000*23250 / 50000 = 5115 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Senior males, we have 10500*23250 / 50000 = 4882.5 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Freshman females, we have 15000*26750 / 50000 = 8025 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For Soph. females, we have 13500*26750 / 50000 = 7222.5 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For junior females, we have 11100*26750 / 50000 = 5885 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic For senior females, we have 10500*26750 / 50000 = 5617.5 Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic So, this is our final set of “Expectation” data (familiar, right!) Here is our “Observation” data. Time to calculate chi square! Gender Freshmen Sophs. Juniors Seniors Males 6975 6277.5 5115 4882.5 Females 8025 7222.5 5885 5617.5 Gender Freshmen Sophs. Juniors Seniors Males 7000 6000 5250 5000 Females 8000 7500 5750 5500 Computing The Chi-Square Test Statistic G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 7000 6975 M. So. 6000 6277.5 M. Jr. 5250 5115 M. Sr. 5000 4882.5 F. Fr. 8000 8025 F. So. 7500 7222.5 F. Jr. 5750 5885 F. Sr. 5500 5617.5 Total Computing The Chi-Square Test Statistic G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 7000 6975 25 M. So. 6000 6277.5 277.5 M. Jr. 5250 5115 135 M. Sr. 5000 4882.5 117.5 F. Fr. 8000 8025 25 F. So. 7500 7222.5 277.5 F. Jr. 5750 5885 135 F. Sr. 5500 5617.5 117.5 Total Computing The Chi-Square Test Statistic G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 7000 6975 25 625 M. So. 6000 6277.5 277.5 77006.25 M. Jr. 5250 5115 135 18225 M. Sr. 5000 4882.5 117.5 13806 F. Fr. 8000 8025 25 625 F. So. 7500 7222.5 277.5 77006.25 F. Jr. 5750 5885 135 18225 F. Sr. 5500 5617.5 117.5 13806.25 Total Computing The Chi-Square Test Statistic G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 7000 6975 25 625 .089 M. So. 6000 6277.5 277.5 77006.25 12.27 M. Jr. 5250 5115 135 18225 3.56 M. Sr. 5000 4882.5 117.5 13806 2.82 F. Fr. 8000 8025 25 625 .078 F. So. 7500 7222.5 277.5 77006.25 10.66 F. Jr. 5750 5885 135 18225 3.10 F. Sr. 5500 5617.5 117.5 13806.25 2.45 Total Computing The Chi-Square Test Statistic G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 7000 6975 25 625 .089 M. So. 6000 6277.5 277.5 77006.25 12.27 M. Jr. 5250 5115 135 18225 3.56 M. Sr. 5000 4882.5 117.5 13806 2.82 F. Fr. 8000 8025 25 625 .078 F. So. 7500 7222.5 277.5 77006.25 10.66 F. Jr. 5750 5885 135 18225 3.10 F. Sr. 5500 5617.5 117.5 13806.25 2.45 Total 35.042 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic So, our next step is to focus on the chi square table again to see if our obtained value of 35.042 is high enough to overcome the critical value Of course, we need to calculate the df once again. For the chi square of independence, the formula is df = (# of rows – 1) X (# of columns – 1) df = (2 – 1) X (4 – 1) df = 1 X 3 = 3 Computing The Chi-Square Test Statistic 2). Computing The Chi-Square Of Independence Test Statistic The df 3 critical value is 7.82 (p < .05) or 11.34 (p < .01) Our 35.042 is clearly over both, so we can say that our gender and year in school observations are significantly different than what we would expect by chance ay p < .01! In fact, it is significant at the p < .00001 level. How do I know that? Well, I cheated a bit and used a computer. I’ll show you that in a moment, I PROMISE! For now, some self-testing … Pop Quiz – Quiz Yourself If we run a two factor chi square of independence looking at employment (employed versus unemployed) and parenthood (has children versus has no children), what df would we use? A). 1 B). 1 and 1 C). 2 D). 2 and 2 E). 3 Pop Quiz – Quiz Yourself If we run a two factor chi square of independence looking at employment (employed versus unemployed) and parenthood (has children versus has no children), what df would we use? A). 1 employment (2 – 1) X parent (2 – 1) = 1 X 1 = 1 B). 1 and 1 C). 2 D). 2 and 2 E). 3 Pop Quiz – Quiz Yourself If we run a two factor chi square of independence looking at employment (employed versus unemployed) and parenthood (has no children versus has one child versus two or more children), what df would we use? A). 1 B). 1 and 1 C). 2 D). 2 and 2 E). 3 Pop Quiz – Quiz Yourself If we run a two factor chi square of independence looking at employment (employed versus unemployed) and parenthood (has no children versus has one child versus two or more children), what df would we use? A). 1 B). 1 and 1 C). 2 employment (2 – 1) X parent (3 – 1) = 1 X 2 = 2 D). 2 and 2 E). 3 Computing The Chi-Square Test Statistic Pause-Problem #1 (Parametric v. Non-Parametric) Let’s see how much you have been paying attention. For your first Pause-Problem in this chapter, please tell me three things that differentiate parametric from non-parametric tests (Hint: There are actually four, so see if you can spot them all!) #1 Part Four Using The Computer To Perform A Chi-Square Test Part Four (A) 1). One Sample Chi-Square Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi Let’s focus on the one sample chi square first Here, we look at only one variable (our variable is “year”, so we assess expected values for Freshmen, Sophomores, Juniors, and Seniors) Forget about gender variable for now for this one sample chi square. We just want to see if the number of students in each year differs from what we would expect by chance. Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi First, we need to enter our data into SPSS Usually, we need one “year” cell for each student Since we have 15,000 Freshmen, I would be entering the number 1 in the “Year” column 15,000 times! (1 = Freshmen) Sorry, I am not that crazy, so I am going to reduce this to 150 for our Freshman for these few slides … Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi First, we need to enter our data into SPSS So this SPSS data set is based on 150 Freshmen (15,000 originally), 135 Sophomores (13,500 originally), 110 juniors (11,000 originally), and 105 seniors (10,500 originally), or 500 total (50,000 originally). Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi First, we need to enter our data into SPSS Remember, this is a nominal variable, so 1 could be Seniors, 2 could be Juniors, 3 could be Freshmen, and 4 could be sophomores The actual “year” number is irrelevant and arbitrary. In fact, SPSS allows me to just look at the label if I want … Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi First, we need to enter our data into SPSS Remember, this is a nominal variable, so 1 could be Seniors, 2 could be Juniors, 3 could be Freshmen, and 4 could be sophomores The actual “year” number is irrelevant and arbitrary. In fact, SPSS allows me to just look at the label if I want … See! Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi Square (One Sample) Second, we click analyze, find the “non-parametric test” option, and find the “Legacy Dialogs” option, which opens up the chi square (one sample) test. Move your variable (“year”) to the “Test variable list” Click “okay” Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi This is the first table in our output. As you see, we get our “Observed N” for each year and our “Expected N” (Expected N is also 500 total, or 500 / 4 = 125 for each year). We also see residuals (Observed minus Expected) Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi This is the second table in our output. Our df is still 3 (four years minus one, or 4 – 1 = 3) Our chi square is 10.800. Our hand calculation was 1080, but in SPSS we dealt with 500 students rather than 50,000, so just move the decimal here and you’ll see we duplicate our answer! Square (One Sample) Using The Computer – The Chi Square 1). Using The Computer To Compute A Chi Square (One Sample) How Would I Write Up This Result In A Results Section? “A chi-square goodness-of-fit test was performed to determine whether FIU students were equally distributed across four years in college. Results showed that the students were not equally distribute, X2(3) = 10.80, p < .01.” Pop Quiz – Quiz Yourself If there is no difference between what is observed and what is expected, your chi-square value will be: A). 0 B). 1 C). -1 D). Cannot be determined Pop Quiz – Quiz Yourself If there is no difference between what is observed and what is expected, your chi-square value will be: A). 0 B). 1 C). -1 D). Cannot be determined Part Four (B) 2). Chi-Square Of Independence Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? IMPORTANT: In your first study (Paper II), you will compare two nominal variables (a nominal dependent variable and a nominal independent variable) to see if the observation differs by chance, so THIS test is the one to use … Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence I am going to get to the SPSS computer analysis in a moment for the chi square of independence, but I just want to mention that there are lots of free online statistical programs you can use for your data For the independent chi square analysis, I found a site that was very helpful in the calculations. Note: The font of the numbers are small in these next tables, but they duplicate the tables we just went through! Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Lots of online programs will do this for you. For example, consider this website, where you enter your observed counts: http :// www.socscistatistics.com/tests/chisquare2/Default2.aspx Blank “Starting” Screen Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Lots of online programs will do this for you. For example, consider this website, where you enter your observed counts: http :// www.socscistatistics.com/tests/chisquare2/Default2.aspx Insert your gender and year (nominal variables) categories Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Lots of online programs will do this for you. For example, consider this website, where you enter your observed counts: http :// www.socscistatistics.com/tests/chisquare2/Default2.aspx This is our original “observed” table for gender and year Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Lots of online programs will do this for you. For example, consider this website, where you enter your observed counts: http://www.socscistatistics.com/tests/chisquare2/Default2.aspx Ta da! Σ (E – O)2 / E to get your 35.04 chi square statistic! Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Lots of online programs will do this for you. For example, consider this website, where you enter your observed counts: http://www.socscistatistics.com/tests/chisquare2/Default2.aspx I promised to tell you how I got p = .00001? Promise kept! Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Unfortunately, dropping our sample from 50,000 down to 500 in SPSS actually impacts the chi square outcome for independent chi square tests when I run it in SPSS Since I don’t want to enter 50,000 participants into SPSS, let me show you the calculation for 500 students instead But first, a friendly reminder of our 50,000 participants … Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Remember this table? It now becomes … Gender Freshmen Sophs. Juniors Seniors Row Total Male 7000 6000 5250 5000 23250 Female 8000 7500 5750 5500 26750 Column Total 15000 13500 11000 10500 50000 Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Remember this table? For the chi square, we multiply each row by each column / n Gender Freshmen Sophs. Juniors Seniors Row Total Male 70 60 53 50 233 Female 80 75 57 55 276 Column Total 150 135 110 105 500 Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Remember this table? An N of 500 is much easier to enter into SPSS than 50,000! Gender Freshmen Sophs. Juniors Seniors Row Total Male 70 60 53 50 233 Female 80 75 57 55 276 Column Total 150 135 110 105 500 Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Remember this table? For Freshmen males, 150 X 233 = 34950 / 500 = 69.9 etc. Gender Freshmen Sophs. Juniors Seniors Row Total Male 70 60 53 50 233 Female 80 75 57 55 276 Column Total 150 135 110 105 500 Computing The Chi-Square Test Statistic Computing The Chi-Square Of Independence Test Statistic Again, here is our “Expectation” data Here is our “Observation”. Now, time to calculate chi square! Gender Freshmen Sophs. Juniors Seniors Males 69.90 62.91 51.26 48.93 Females 80.10 72.09 58.74 56.07 Gender Freshmen Sophs. Juniors Seniors Males 70 60 53 50 Females 80 75 57 55 Using The Computer – The Chi Square G / Yr. Observe Expect Difference (O – E)2 (O – E)2 / E M. Fr. 70 69.90 .10 .01 .00 M. So. 60 62.91 2.91 8.47 .13 M. Jr. 53 51.26 1.74 3.03 .06 M. Sr. 50 48.93 1.07 1.44 .02 F. Fr. 80 80.10 .10 .01 .00 F. So. 75 72.09 2.91 8.46 .12 F. Jr. 57 58.74 1.74 3.02 .05 F. Sr. 55 56.07 2.07 1.07 .02 Total .407 Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? Here, our chi square for independent samples gives us .407 (you can see this below from the online calculator as well as in the table in the previous slide) Now, let’s see the SPSS version Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? In SPSS, we use a different procedure than the one sample chi square to look at a chi square test of independence. In SPSS, first go into “Analyze”, then “Descriptive Statistics”, and find the “Crosstabs” statistical test A BIG NOTE HERE: You will do this SPSS test for Paper II with your study one, so pay very close attention! Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? Move “Year” and “Gender” to the correct column It doesn’t matter which goes where Next, click the “Statistics” button Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? In “Statistics”, select the “Chi Square” as well as “Phi and Cramer’s V” Then click continue and then okay Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? Our first table is the crosstabulation table. This simply tells us how many variables fall into each cell (70 male freshmen, 60 male sophomores, etc. Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? Our second table is more important: our Chi Square table Focus on Pearson: It is NOT significant, with df = 3 and a value of .407 (p = .939) Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence What about our independent samples chi square? So SPSS found the same thing as both our hand calculation for 500 students and our online calculator (some rounding is involved to get us to that .407, of course!) The final table looks at phi. Phi is essentially a correlation, ranging from 0 to +1. A low phi (.029) means there is little correlation between our two nominal variables here Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Writing up our non-significant chi square test of independence “There was no significant relationship between gender and year in school. X2(3) = .407, p > .05. The number of males and females did not differ from chance when taking into account their year in school.”
X2 is our chi square test and value
3 is our degrees of freedom, or (2 – 1)*(4 – 1) = 1 X 3 = 3
p < .05 is our significance level Using The Computer – The Chi Square 2). Using The Computer To Compute Chi-Square of Independence Writing up our non-significant chi square test of independence Imagine there was significance (Pearson value was 18.26 and p = .0023). This is what that write-up would look like: “There was a significant relationship between gender and year in school. X2(3) = 18.26, p > .05.”
In your lab slideshow, I will show you an even more precise way of looking at percentages, but this is good for now

Using The Computer – The Chi Square
2). Using The Computer To Compute Chi-Square of Independence
Writing up our non-significant chi square test of independence
Imagine there was significance (Pearson value was 18.26 and p = .0023). This is what that write-up would look like:
“There was a significant relationship between gender and year in school. X2(3) = 18.26, p > .05.”
Of course, I want to see if you can do a write-up similar to this on your own! Time for your second Pause-Problem …

Using The Computer – The Chi Square
Pause-Problem #2 (Computer Output):
Let’s say you design a study looking at cell phones. You ask participants what their current cell phone brand is and what brand of phone they would LIKE to have. You get this …

Now, consider your Chi Square table …

#2

Using The Computer – The Chi Square
Pause-Problem #2 (Computer Output):
Chi Square Test of Independence

Using these two tables, write out the results as you would see them in a results section of an APA formatted journal article

#2

Part Five
Other Nonparametric Tests You Should Know About

Other Nonparametric Tests
Other Nonparametric Tests You Should Know About
Sometimes we use nonparametric tests when we have nominal variables (as we saw here), but other times you might use such tests when …
1). You do not have a normal curve (and thus you cannot use a t-Test or ANOVA, which rely on normal distributions)
2). You have a sample size smaller than that required by either a t-Test or an ANOVA
3). There are other violations of the assumptions underlying parametric tests

Other Nonparametric Tests
Other Nonparametric Tests You Should Know About
Table 17.1 in your Salkind textbook (page 360) lists several nonparametric tests, including tests like …
Categorical Data Tests (nominal data) :
McNemar Test For Significance of Changes
Fisher’s Exact Test
Chi-Square One Sample Test (which we covered in this presentation)

Other Nonparametric Tests
Other Nonparametric Tests You Should Know About
Table 17.1 in your Salkind textbook (page 360) lists several nonparametric tests, including tests like …
Rank-Ordered Data Tests (ordinal data)
Kologorov-Smirnov Test
The Sign or Median Test
Mann-Whitney U Test
Wilcoxon Rank Test

Other Nonparametric Tests
Other Nonparametric Tests You Should Know About
Table 17.1 in your Salkind textbook (page 360) lists several nonparametric tests, including tests like …
Rank-Ordered Data Tests (ordinal data)
Kruskal-Wallis One Way ANOVA
Friedman Two Way ANOVA
Spearmen Rank Correlation Coefficient

Other Nonparametric Tests
Other Nonparametric Tests You Should Know About
We are not going to cover these in this course, but just be aware that they exist (especially if you go on to become an academic!)

Using The Computer – The Chi Square
Pause-Problem #3 (A Chi Square Study)
Now that you have a better idea about what differentiates a one sample chi square from an independent samples (two factor) chi square, I want you to come up with one study idea that would use a one sample chi square and one study that would use an independent samples (two factor) chi square
One restriction here: You cannot use your lab study idea

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Part Six
An Eye Toward The Future

An Eye Toward The Future
Here your last Pause-Problem #4 (Pop Quiz)
Yup, this slide again!
For your last Pause-Problem, I want YOU to write a multiple choice pop-quiz question based on the content of this chapter. I might use your question on a future pop quiz or actual course exam (though not this semester), so make it good! Make sure to include your correct answer and up to five possible answers!

#4

An Eye Toward The Future
An Eye Toward The Future
Make sure you fully understand the chi-square here, as you will analyze some of your study one data using this procedure
You should be all set with regard to your results section, as you now know all about descriptive statistics (mean, the standard deviation, chi square) and inferential statistics (t-Test, ANOVA)

An Eye Toward The Future
An Eye Toward The Future
Next week, though, I want to return to an earlier Smith and Davis chapter, Chapter 4 (Non-experimental methods).
As you start to work on materials for your second study in your labs, you’ll learn how to create questionnaires and surveys as you work through the Chapter 4 sections.

An Eye Toward The Future
Finally, it is VERY, VERY, VERY important for you to read your lab presentation immediately. Since many of your papers are based on content covered in the lab, you need to know about that content sooner rather than later
So, here is your reminder to read that lab presentation immediately