T test and ANOVA
By
jen ripley
Created 3 years ago
Duration 0:57:28
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A review of t test and basic concepts in ANOVA

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Psychology Statistics

Slide 1  Comparing Groups data
 Dwarves vs. Minions Which are better?

Slide 2  Objectives
 When to use stat
 Independent vs. paired samples
 Within/Between design
 Calculate a df
 Why is multiple t test bad?
 One tails vs. two tails
 Orthogonality
 Assumptions of all stats
 How to report stats
 When to use different stats for assumptions
 What do the numbers mean when reported?
 Followup options in ANOVA, when & what?

Slide 3  A study
 What’s the difference between Prozac and Ketamine in treatment of depression symptoms?
 Prozac= 6.58
 Ketamine= 9.77
 What is the IV?

Slide 4  What should Dr. Williams do?
 The researcher has two independent samples the behavior in one sample is not related to the behavior in the other sample.
 She could run an independent samples T test to compare the two (and only 2) means and see if they are significantly different.
 What is her research question?

Slide 5
 Research Question: Does type of drug affect (Prozac vs. Ketamine) depression symptoms?

Slide 6  Categorical IV Continuous DV
 What is Dr. Williams doing?
 Comparing the distribution of one group with the distribution of the other group to find that point, or critical value, where group differences are improbable (p<.05) as a function of chance

Slide 7  Remember the importance of type of distribution: These have the same mean scores

Slide 8  Remember it matters both mean and variance/distribution of your two groups
 Ketamine
 Prozac
 Ketamine
 Prozac
 Ketamine
 Prozac
 Looking really different
 Probably different at p<.05
 Are they different with
 P<.05?

Slide 9  Variance (spread) & Ttest
 When we are looking at the differences between scores for two groups, we have to judge the difference between their means relative to the spread or variability of their scores.
 The ttest does this.
 Compare two groups’ means and variances. Each group has its’ own sample size too.

Slide 10  Formula
 N= total number of participants, n= number of participants within a group
 Numerator is just difference between means
 Denominator “ingredients” is variance (square of standard deviation) plus n= number of participants
 What you need to know: The t value is not just difference between means but also accounts for variance and sample size

Slide 11  Explain to your neighbor
 For a t test to be significant what do you need in terms of mean and variance?
 Come up with another study that could be a t test what is the IV and DV?

Slide 12  Degrees of Freedom
 Depends on degrees of freedom (df): number of values in a set of scores that are free to vary after certain restrictions are placed on the data.
 For a mean score , if you were to sum up all the differences between each score in a study and the mean they would equal 0.
 Suppose we have just 5 scores in a distribution, 4 people give me a deviation from the mean (+ or ).
 What’s the 5th score have to be (hint=total has to be 0) so 4 numbers could be ANY number, while 1 number must be the same, n1=4

Slide 13  https://www.youtube.com/watch?v=iA2KZHHZmmg A good 6 minute review of DF in statistics.

Slide 14  Degrees of Freedom
 If the mean of a set of 3 collected variables is 11 there’s an infinite number of options to get that mean (11,11,11..10,11,12)
 If I say one of those numbers is a 7 then it’s still infinite for the other two numbers
 If I tell you one is 7 an the other is 10 there is only one possible value for the third number
 So for this problem there is 2 degrees of freedom. Once two numbers are determined then the third number is fixed.

Slide 15  Let’s Experiment…
 Mean shoe size is 8
 Frequency distribution of 5 people: 2, 5, 10, 11
 What does the fifth person’s size have to be?
 How many degrees of freedom in this problem?
 Tell your neighbor your answer see if you got it right.
 Formula for df:
 For one group df= n1
 For two groups df = n2

Slide 16  T Test Please
 Dr. Williams wants to know if the two groups are different and her sample is small df=N2 (because 2 groups).
 So if she has 26 people in the experimental (ketamine) group and 26 people in the standard (Prozac) group her df is?
 50
 e.g., t(50)=4.3
 Note: Degrees of freedom in t test will tell you how many participants were in the study ;)

Slide 17  Just for Fun
 Interesting side story: The “inventor” of the T test, Gosset (1899), was motivated because he was brewing beer for Guinness in Ireland and wanted to know what kind of barley to use to make the product more consistent. He used the pseudonym “student” so Guinness wouldn't have to own up.

Slide 18  Next Step:
 Between or within subjects design?

Slide 19  Between vs. within subjects design
 Between subjects randomly (hopefully) assigns all participants to one group
 Either you get Ketamine or Prozac for the study
 Within subjects design allows everyone in the study to spend time in each condition/level of the IV
 You get one drug for a while, and then you get the other drug for a while
 This is a design issue that you need to know to tell your computer which version of T test you should run

Slide 20  Assumptions of t test
 1 Categorical IV (2 cats)
 1 Continuous DV
 Robust to violations of assumptions in general… can be “liberal”

Slide 21  Assumptions of t test
 N unequal n problem for small sample
 Normality Important for small sample size or low power; Not so important for moderate to large sample size.
 What’s small? Let’s use power analysis to decide…

Slide 22  Homogeneity of variance
 Homogeneity of variance a little important, but less so as sample gets larger
 Levene’s test will show up in SPSS output for you automatically

Slide 23  Homogeneity of Variance
 In Independent Samples
 For between subjects design it is very important

Slide 24  Violate Multiple Assumptions
 Homogeneity of Variance + Unequal n (two groups different sizes)
 If both violated, you have a real problem. Puts all your statistics in question.

Slide 25  Self Test
 What is ttest doing?
 What are degrees of freedom?
 Come up with another example study that would be appropriate for a T test.
 Give example of heterogeneity of variance and unequal sample size
 Any questions?

Slide 27  ANOVA does what?
 Categorical IV (2 or more cat)
 ONE continuous DV
 Are the groups different?
 Between or within subject design possible

Slide 28  What am I doing?
 Low within group variability and high between group variability produces a significant effect
 High within group variability and low between group variability produces no effect

Slide 29  Graph
 Ketamine
 Prozac
 High between group variability
 Mod low within group variability
 Ketamine
 Prozac
 Low between group variability
 High within group variability
 Depression severity score
 Depression severity score

Slide 30  ANOVA
 What is it doing?
 It’s significant when?
 Mean and variance are both involved

Slide 31  Assumptions
 Independence of Scores (scores not related within groups or between groups)
 Normal distributionalthough ANOVA procedure is pretty robust and could transform variables if skewness is a big problem
 Equal sample sizes can be important, especially if not otherwise robust design
 Homogeneity of Variance (especially if unequal sample sizes)
 If really not passing the normality assumptions, & don’t want to transform would do another analysis (e.g., KruskalWallis test)

Slide 32  Homogeneity of Variance
 Levene’s test: SPSS default. Examines variance (Runs an ANOVA) based on deviations from the mean. Not significant is good.
 BrownForsythe test: Option in SPSS. Less deficiencies. Examines variance (Runs ANOVA) deviation from the group median.
 Welch test: Similar to BrownForsythe.
 Caveat: BrownForsythe & Welch not satisfactory if more than 4 groups
 Then do James’s second order method or twostage method (Keppel), maybe
 Lack of agreement among statisticians of WHEN heterogeneity is a problem

Slide 33  Reporting ANOVA
 Report this for T=test or ANOVA
 Size of each group
 Skewness & kurtosis of DV
 Test of homogeneity of variance
 Degrees of freedom
 Sum of Squares (rarely report in ANOVA)
 Mean of Squares (rarely report in ANOVA)
 F ratio (ANOVA), tvalue (ttest)
 p value
 Group means (and standard deviations often)

Slide 34  Followup Analyses 2,3,4,5… groups
 Once you know there are differences, how do you know which group is different than the others if you have more than 2?
 F test will not answer this question unless…
 If just two groups, just look at mean scores. Ex. Gender
 If more than two…
 Planned contrasts (orthogonal is best)
 Trend analyses
 Posthoc tests: Tukey or Scheffe
 Examine means

Slide 35  Planned Comparisons
 Two treatment groups vs. control group
 Parents of infants & toddlers vs. Parents of school age & high school children
 Must be orthogonal to compare treatment vs. no treatment: +1/2 standard + ½ experimental + 1 control group (the numbers rep. coefficients in formula)
 Must always sum = 0
 Planned not posthoc

Slide 36  Orthogonality Example
 Planned Comparisons OK
 Parents of infants groups plus parents of toddlers group vs. Parents of school age plus parents of teen group
 Parent of infants vs. parents of school age
 Parents of school age vs. parents of teens
 NOT OK
 Parents of school age and teens vs. parents of school age and toddlers
 No “double dipping”

Slide 37  Post hoc Test options
 Tukey & Scheffe (slightly different stat methods)
 Both compare means for all groups and tell you which ones are sig. different
 Powerful & Robust analyses (don’t need to do Bonferroni’s for these)
 Will give you minimum sig. difference number

Slide 38  Why not always do posthoc?
 Method is not planned a priori

Slide 39  Self test
 How is t test different than ANOVA?
 Come up with another example of an ANOVA with 3 levels of one IV
 How do you do apriori and posthoc tests when you have 3 or more groups in your IV?
 What assumptions should be tested for an ANOVA?
 There are two assumptions that if both are violated we have a bigger problem? What are they?

Slide 40  What to Know from Lecture
 When to use stats
 Independent vs. paired samples
 Within/Between design
 Define terms
 Calculate a df
 Why is multiple t test bad?
 One tail vs. two tails
 What is an F ratio ?
 How to compare groups when you have 3 or more groups
 All assumptions
 Assumptions of all stats
 How to report stats
 When to use different stats for assumptions
 What do the numbers mean when reported
 Fratio
 Followup options in ANOVA, when & what

Slide 41
 Prayer Requests and Questions?