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What are the assumptions of a single sample t test?

1. normally distributed
2. randomly selected
3. at least interval data


What are the assumptions of an independent samples t test?

1. sampling distribution of scores in each group is normally distributed
2. groups are randomly selected and independent
3. equality of variances (homogeneity of variance)
4. at least interval data


What are the assumptions of a dependant samples t test?

1. sampling distribution of differences between scores is normally distributed
2. randomly selected
3. at least interval data


How do you calculate the effect size for a single sample t-test

effect size (Cohen's d) is
Mean difference (observed mean minus population mean)
population standard deviation

t statistic OVER square root of N


What is Levene's test for equality of variances and how does it affect how the SPSS output for a t test is interpreted?

which type of t test does this apply to?

[note only applied to independent samples t test]
It tests the hypothesis that the variances in the two groups are equal (i.e. the difference between the variances is zero)

If the output shows Levene's test as being significant then we assume that there is a significant difference in variances (i.e. that the assumption of equality of variances has been violated)

-> if violated read the output from the row 'equal variances not assumed'


How do you calculate the effect size for an independent samples t-test?

Cohen's d =

Mean difference OVER pooled population standard deviation



What is eta squared?

Eta squared (η2) is a measure of the variance accounted

-> The variance in the in the dependent variable accounted for by the independent variable


How do you calculate the effect size for a dependent samples t-test?

Cohen's d = mean over population SD

d = t/square root of n

NOTE: make sure not to put top or bottom in parentheses


How do you calculate eta squared (η2) for an independent samples t test?

tsquared + (n1+n2-2)

note the n1 and n2 should be subscript numbers - not multiplying by 1 and 2

NOTE calculator -> put top in parentheses and put bottom in parentheses


How do you calculate eta squared (η2) for a dependent samples t-test?

tsquared + n-1

NOTE absolutely can't figure out how to make this work on my calculator
SOLUTION: calculate t squared and use that to plug into calculator manually


How is eta squared interpreted?

Eta-squared ranges from 0 to 1 and indicates the proportion of overlap between the
grouping variable (the IV) and the outcome variable (the DV). It is often reported like
“the independent variable explained 15% of the variance in the dependent variable.”
Cohen’s conventions for eta-squared are: .01 small, .06 = medium, .14= large.


Why would you perform an ANOVA rather than multiple t tests?

give an example

because multiple analyses increase the likelihood of committing a type 1 error

e.g., if we did 5 independent analyses (i.e. 5 t tests) and the probability of a type one error (alpha) was set at .05 for each -> you would sum those probabilities and get a .25 chance of committing a type 1 error (note because they are combined with OR)


What are the assumptions of a one way ANOVA

1. normally distributed within each group
2. randomly selected, representative sample
3. homogeneity of variance
4. at least interval data


What effect measure is used for ANOVA and why?

Eta squared - cannot use Cohen's d when there is more than 2 groups


How do you calculate and interpret the effect measure (Eta squared) for an ANOVA

Sum of squares treatment
Sum of squares total
SPSS output SS between groups OVER SS total

Need to compare it to something to be able to know if the effect is typical

(e.g. in slides is .19 -> IV explains 19% of variance in IV but can't interpret unless given context)


What is the The Brown and Forsythe Test?

Also known as the modified Levene test - it is a test for equal population variances

Robust test based on the absolute differences within each group from the group median


What is Welch's Test?

an alternative test for the one factor analysis of variance F test. It is a test for equal population means to be used when we do not have equal population variances. It is a parametric test


What is an ANOVA test and what is the statistic it provides?

ANOVA tells us whether three or more means are the same, so it tests the null hypothesis that all group means are equal

F statistic which compares the amount of systematic variance in the data to the amount of unsystematic variance (similar to t)


What is a Fixed factor?

A factor is fixed when the levels under study are the only levels of interest

Typically things that are set by researchers -> e.g. looking at 3 doses of a medication and 'dose' is the factor


What is a Random factor?

A factor is random when the levels under study are a random sample from a larger population and the goal of the study is to make a statement regarding the larger population

e.g. studying the effects of machine operator on productivity by taking a random sample of operators and assessing the variability attributable to the factor 'operator'


What does partial Eta squared indicate in a factorial ANOVA? How is this different from eta squared?

For a factorial ANOVA: the variance accounted for by the variable of interest given the presence of other main effects and interactions.

Because there are other interactions to account for, the eta squared calculated only accounts for the variance accounted for by that variable of interest and not the others.


In a simple ANOVA what is the difference between Eta squared and partial eta squared?

they are equal (no difference)


What is the difference between a simple ANOVA and a factorial ANOVOA

a one-way (simple) ANOVA has one independent variable that splits the sample into two or more groups

a Factorial ANOVA has two or more independent variables that split the sample in four or more groups


What do you need to be careful of when interpreting SPSS generated graphs?

The scaling -> usually not done with a zero point so it makes the effect look more dramatic


What is the statistic an ANOVA produces and what does it represent?

The F-ratio

This is a ratio of the variation explained by the model over variation explained by unsystematic factor