C. 8 Statistical Inference


Descriptive statistics

- to describe data
- central tendency, variability, skewness, kertosis

Inferential statistics

- to make inferences about population from sample
- attempt to find out causation

If IV has 2 levels or conditions

Do z ratio or t test

If IV has >2 levels or conditions


Do z ratio for:

proportions and large samples

Do t test for:

means and small samples

Z score table

1. find first 2 digits of z score on left side of table
2. look up remaining # on top of table
3. find corresponding area which translates to %
4. % is area left of z score, meaning score is that % better than general population (almost like percentile)

T distribution table

* need to know degrees of freedom of t test, # tails of t test, alpha level of t test
1. degrees of freedom is n-1
2. find degree freedom on left
3. find alpha level at top
4. find corresponding area for both

Independent t test

for comparing 2 independent groups

Dependent t test

aka paired sample; use when one sample of participants is measured twice under 2 different conditions (ex. pre & post test) OR when samples are pair matched

Mann-Whitney U test

nonparametric independent t test

Wilcoxon t test

nonparametric dependent t test


- test for differences among several means
- IV has >2 levels or conditions
- F ratio
- trying to answer if there is a difference among a set of group means --> in order to say yes, variance between groups needs to be significantly larger than variance wi

1 way ANOVA

effect of 1 IV on DV

2 way ANOVA

effect of 2 IV on DV

4 x 2 ANOVA

2 IV, 1 has 4 levels & other has 2 levels

3 x 3 x 3 ANOVA

3 IV, each has 3 levels

If there is more than 1 DV, use:


If studying effect of 1 IV on 1 DV but think other factor(s) could effect DV too:


Criteria for parametric

- population normally distributed
- interval or ratio measurement
- variances of data about same
- large enough sample

Coefficient determination

r^2, estimates effect size

Eta squared

n^2, interpreted same as coefficient determination

Partial eta square

used for multiple IVs on 1 DV

Typical effect sizes

0.2 = small
0.5 = medium
0.8 = large


related to type II error (accepting a false null)
power = 1 - type II

Increased power leads to

increased probability of correctly rejecting a false null

A priori

done before data collection, determines sample size

Post hoc

further evaluates completed research to determine if failure to reject was due to inefficient sample size