PALS0046: Intro to Statistical Methods - T-tests

When to use t-tests?

When testing the relationship between a binary independent variable (2 groups) and a numeric dependent variable

What are the three types of t-test?

- 2 samples t-test

- Paired samples t-test

- One sample t-test

When is a two samples t-test used?

When there is a binary categorical variable that is between-subjects design, and a numeric outcome variable (and you want to know whether there is a relationship between the two)

How is a two samples t-test calculated?

Mean of group 1 vs mean of group 2

When is a one sample t-test used?

1 variable, and you want to know whether the mean for that variable differs from a specific value - 1 group vs population mean

When is a paired samples t-test used?

Similar to two sample t-test, but categorical predictor is within subjects instead of between subjects

How is a paired samples t-test calculated?

Means of both groups calculated

T-statistic

indicates the distance of a sample mean from a population mean in terms of the estimated standard error

How to calculate t-statistic?

t = effect/error = difference between means/standard error

Standard error formula

se = sd/sqrt(sample size)

Define T-statistic

Measure of difference between means taking into account the variability in the data; larger the difference between means, the larger t (higher confidence in our mean difference); larger variability, smaller t (lower confidence in our mean difference)

Calculating one sample t-value

t = (sample mean - hypothesised population mean) / (sd/sqrt(sample size))

Null hypothesis distribution re: t-tests (3)

- For large samples, distribution of H0 t-values has the standard normal distribution

- For smaller samples (fewer degrees of freedom), t-distribution has fatter tails

- BECAUSE we don't know true population standard deviation and our sample SD underestimates population SD

Paired sample t formula

t = (sample mean difference - 0)/ (sample standard deviation difference / sqrt(sample size))

Cohen's D

a measure of effect size indicating how far apart two group means are, in standard deviation units

Cohen's d formula

Cogen's d = mean difference / standard deviation

Assumptions of t-test (4)

- DV is interval or ratio level (Likert scales are quasi-interval)

- DV is normally distributed (in each group if 2 sample test, the difference if paired sample test)

- For two-samples test: the 2 samples are independent

- For paired-samples test: the 2 samples are paired

Student's t-test vs Welch's t-test

Students t-test assumes equal variances (assumes the standard deviations of the two populations will be equal even if means differ)

One-sample t-tests

Test the hypothesis that a population mean is different from a known or theoretical population mean

Two-sample t-tests

Test the hypothesis that 2 samples come from 2 different underlying populations

Paired sample t-tests

Used when you have a within-subjects dichotomous predictor

All types of sample t-tests require....

Outcome variable that is interval or ratio level

Assumption across all t-tests

Outcome variable is normally distributed