T Distribution

The critical value (tcrit) is determined based on

degrees of freedom = (N - 1) where N equals the number of difference scores • The selected α, and • whether a one-tailed or two-tailed test is used

Critical values for the independent samples t-test (tcrit) are determined based on

degrees of freedom: df = (n1 - 1) + (n2 - 1) • the selected α, and • whether a one-tailed or two-tailed test is used

t distribution

distribution of all possible values of t computed for random sample means selected from the raw score population described by H0

If t(obt)>t(crit)

reject the null hypothesis

one-sample t-test

s the procedure used for a one-sample experiment when the standard deviation of the raw score population must be estimated.

matched-samples design

the researcher matches each participant in one condition with a participant in the other condition • We do this so that we have more comparable participants in the conditions

Steps to Calculate The Test Statistic for an Independent Samples T-Test

1. Calculate the estimated population variance for each condition 2. Compute the pooled variance 3. Compute the standard error of the difference 4. Compute tobt for two independent samples

Independent Samples T-Test Assumptions/Requirements:

1. The dependent scores measure an interval or ratio variable. 2. The populations of raw scores form normal distributions. 3. The populations have homogeneous variance. Homogeneity of variance means the variances of the populations being represented are equal. 4. While ns may be different, they should not be massively unequal.

Setting Up the One Sample T-Test

Check the assumptions for a t-test. . . • Set up the statistical hypotheses (H0 and HA). • Select alpha. α = .05 is typically used.

Transforming Raw Scores

In a related-samples t-test, the raw scores are transformed by finding each difference score • The difference score is the difference between the two raw scores in a pair • The symbol for a difference score is D

Independent Samples T-Test

Tests whether two groups/variables have statistically significantly different means • Participants can only be in one of the two groups • Ex: Those currently living in Missouri vs. those currently living outside of Missouri

Assumptions of Paired Samples T-Test

The dependent variable involves an interval or ratio scale • The raw score populations are normally distributed • The populations have homogeneous variance • Because related samples form pairs of scores, the n in the two samples must be equal

Paired samples

The paired samples t-test is the parametric inferential procedure used with two related samples • Also known as a related samples t-test • Paired samples occur when we pair each score in one sample with a particular score in the other sample • Two types of research designs that produce paired samples are matched-samples design and repeated-measures design

One Sample T-Test Degrees of Freedom

The quantity N - 1 is called the degrees of freedom • We obtain the appropriate value of tcrit from the t-tables using both the appropriate α and df

One Sample T-Test Statistic

Tobt= (x-u)/Sx

Assumptions for a one sample t-test

You have one random sample of interval or ratio scores • The raw score population forms a normal distribution • The standard deviation of the raw score population is estimated

repeated-measures design

each participant is tested under all conditions of a given independent variable.

As sample size grows

you need a smaller t-value to reach significance

To maximize power in the independent samples ttest, you should

•Maximize the size of the difference between the means •Minimize the variability of the scores within each condition •Maximize the size of N, that is, n1 + n2