Module 4 - comparing 2 groups, Student's T Distribution

When do you use Student's T Distribution

unknown pop. standard deviation, sample size < 30

Law of errors

as sample size decreases -> likelihood sample mean = true pop mean decreases

Characteristics of Student's T distribution

mean = 0, symmetric around mean, total area= 1, area under curve change as sample size change

2 sample T test

compare means of 2 samples

Dependent T test

compare 2 dependent groups - have differences?

self-paired groups

2 measurements on same subject at 2 time points

matched pairing

groups matched on 1 characteristic

Assumptions of Dependent T-test

dependent variable = scale measurement, pairs= independent from another, normal distribution

Interpreting Output of Dependent T-test

95% CI - if include 0 or not (0=likely no differences), t-score (neg or pos = what side of mean) + df -> compare to t chart, Sig ( 2-tailed) = p-value

Independent T-test

comparing 2 independent groups - have differences?

Assumptions of Independent T test

dependent variable = scale measurement, 2 independent samples, normal distribution, homogeneity of variance

Homogeneity of variance

equal variance in both samples

Levene's Test

check for equal variance, null hyp: equal variance

Interpreting Output Independent t-test

95% CI - if include 0 or not (0=likely no differences), t-score (neg or pos = what side of mean) + df -> compare to t chart, Sig ( 2-tailed) = p-value, includes Leven's Test

Parametric tests

make assumptions about population sample is drawn from

non-parametric tests

don't make as many assumptions, 'distribution-free'

Wilcoxon Signed Rank

Non parametric test for comparing 2 dependent samples

Mann-Whitney U test

non parametric test for comparing 2 independent samples

Categorical Analyses

compare proportions between groups, chi-squared test

Two-Way Contingency Tables

compare counts between dichotomous variables, INSERT IMAGE

Chi Square Test

compare proportions between 2 independent groups

characteristics of chi square distribution

positive values, defined by df, mean = df, variance = 2xdf, mode = df-2 (df >=2)

how calc df for chi square

(# of rows - 1)(# of columns - 1)

Assumptions of chi-square test

data = count/frequencies, groups = independent & mutually exclusive, df >= 1, no >20% of cells have

Fisher's Exact Test

compare proportions between 2 unpaired groups (independent) but >20% of cells have

McNemar's Test

compare proportions between 2 paired groups (dependent)