Review Outline – Exam 2 – Psy 340 (Fall 2006)
Ch 7 – One-Sample t-test and Dependent Samples t-test
o 1-Sample t-test used when comparing sample mean to population mean, but population
standard deviation is unknown.
 Use S2 to estimate population variance
 Then find S2M and SM (variance and standard deviation, respectively, of the
distribution of means).
 T obtained formula: (M - ) / SM
 Find critical t value from T-table, using degrees of freedom (N-1), alpha, one-two
tailed test.
o

Dependent Samples t-test used when comparing two means but from same sample. Will
create ‘difference’ scores for each person.
 Null hypothesis is that there is no difference (=0)
 Find mean of difference scores, S2 and SM for difference scores.
 T obtained = (M - ) / SM……note that  is always 0 (your comparison)
 Know how to interpret SPSS output for dependent samples?
See “Review Activity” file for sample practice problems to cover in class 10/26
Ch 8 – Independent Sample t-test
o Here comparing two means from two different samples. Null hypothesis is that there is no
difference between the two groups.
o First find pooled estimate of population variance (S2 pooled)
o Next find S2M1 and S2M2 (for each group)
o Then find S2Difference and SDifference
o T obtained = (M1 – M2) / S difference
o Use t table to find critical t, note that df = N-2.
o What is the harmonic mean (conceptually)? Why do we sometimes need to figure it?
o Know how to interpret SPSS output for this. Remember that SPSS checks the assumption of
equal group variances. First determine if that is true or if the assumption is rejected. Then follow
the appropriate line to get your output for the obtained t.
o
See “Review Activity” file for a sample practice problem and SPSS output to cover in class 10/26
Ch. 9 – Introduction to ANOVA




When is ANOVA used? Testing differences between means of more than 2 groups
o What is the null hypothesis? No group differences (all means are equal)
Focus on estimating 2 sources of variance in scores:
o Within-groups estimate of population variance
 Why would scores vary based on within-group variance?
o Between-groups estimate of population variance
 Why would scores vary based on between-group variance?
When null hypothesis is true, what does the ratio of between-groups: within-groups variance
equal?
When research hypothesis is true, what does the ratio of between-groups: within-groups variance
equal?


Concept of the F ratio (Between groups variance / Within groups variance)
How do you carry out an ANOVA with equal group sizes?
o Find within-groups variance: start with estimates of each group’s variance (S2), then
average those estimates to get S2within aka MS within (see formula in chapter).
o Find between-groups variance: start with estimate of variance of the distribution of means
(S2M); first find Grand Mean (GM), then subtract GM from each group mean and square
that deviation, then add all deviation scores:
 S2M = [ (M – GM)2] / Number of groups – 1.
o Next, use S2M and multiply by group size …this gives you S2 Between aka MS Between.
o Finally, find F obtained by using MS within and between:
 F obtained = MS Between / MS Within
 Compare to F critical where DF numerator = Number of groups – 1 and DF
denominator = (n1 – 1) + (n2 – 1) + (n3 – 1) + ….
 If F obtained > F critical  reject null

Planned Comparisons are next…if you find a significant overall F test, need to follow-up to
determine which groups differ:
o Estimate within-groups variance (as above), then estimate between-group variance but
using only the 2 means of interest.
o Figure F obtained as before (MS Between / MS Within)
o F critical is found using DF numerator (as # groups in comparison – 1); DF denominator
is same as for overall F test (your overall df within).

Bonferroni correction – why/when do you need to do this? How does it control the Type 1 error
rate?
o What do you divide your alpha level by to make the correction?
o What do you do with this new/adjusted alpha level?
o
o
o
Scheffe correction is another possibility…it adjusts your F obtained rather than alpha
level (as in Bonferroni)
For Scheffe, figure F obtained in usual way as above, then divide that F obtained by the
overall study’s DF between (aka DF numerator) which is # total groups – 1.
Compare this adjusted F obtained to the F critical as usual

Effect size in ANOVA is R2 or 2 (eta-squared)…what does it mean? Interpret it in terms of % of
variation in scores due to the group differences.
o What is a small effect size? Medium? Large?

SPSS Output- understand output for a 1-way ANOVA – interpret the overall F test as well as any
Bonferroni follow-up test that appear in the output.

Suggested practice problems for this chapter are #5 (part a and e-i for planned comparisons
with Bonferroni correction)
** Integration – be sure that you can identify which of the 3 t-tests (1-sample, dependent samples,
independent samples) would be the most appropriate test given a description of a study. Also be able to
distinguish between situations when you should use a 1-sample z test versus a 1-sample t test (depends on
whether the population variance is known!) and the benefit to using an ANOVA rather than multiple
independent samples t-tests.