Statistics 4: Hypothesis test between groups (categorical variable and numerical variable)

I. INDEPENDENT SAMPLE T TEST

Independent-samples t test assumes the distributions of a (or more) variables in two groups is same. (untold assumption: the internal nature of the group is the independent variable)

condition: two indepedent samples take one test only.

t(58)=-1,14, p>0.05

1. df (degree of freedom)=n1+n2-2

2. p value

3. one-tailed or two-tailed test

Effect size (ES) is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity. An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population. In that way, effect sizes complement inferential statistics such as p-values. In certain sense, that means p-value tell you the probability to take the wrong decision to reject or accept the null hypothesis, while effect size or correlation coefficient tells you strength of the relationship between variables.
Cohen's d: (X1-X2)/SD
http://www.uccs.edu/~faculty/lbecker/

II. ANOVA (SIMPLE ANALYSIS OF VARIANCE / ONE WAY ANALYSIS OF VARIANCE)

One-way analysis of variance assumes the distribution of a (or more) variables in more than two groups is same. 

condition: more than two groups take one test (one variable).

F(2,27)=8.80, p<0.05

1. df (between)=k-1; df (within)=N-k; df(total)=N-1

2. p value

3. only two tailed test

To determine where is the difference, run post-hoc test with Bonferroni analysis

III. FACTORIAL ANALYSIS OF VARIANCE

Factorial analysis of variance assumes the distribution of a (or more) variables in more than two groups categorized by two variables is same.

Main effect and interaction effect

SPSS use univariate analysis of variance, for it concerns only one explained variable or one dependent variable. 

*if more than two variables, Holy Grail Analysis of Variance

IV. PARED SAMPLE T TEST

Pared sample t test assumes the distribution of a (or more) variable in one group before and after an experiment is same. (untold assumption: the experiment is the independent variable)

condition: only one group takes two tests.

t(24)=2.45, p<0.05

1. df=n-1

2. p value

3. one tailed or two tailed test.