Comparing Two Means: One-sample & Paired-sample t-tests Lesson 12

Inferential Statistics n Hypothesis testing l Drawing conclusions about differences between groups l Are differences likely due to chance? n Comparing means l t-test: 2 means l Analysis of variance: 2 or more means ~

Comparing 2 means: t-tests n One-sample t-test l Is sample likely from particular population? n Paired-Sample t-test l 2 dependent (related) samples n Independent-samples t-test l 2 unrelated samples ~

The One-sample t-test n Evaluating hypothesis about population l taking a single sample l Does it likely come from population? n Test statistics z test if known t test if unknown ~

t statistic

Example: One-sample t-test n Survey: college students study 21 hr/wk l Do Coe students study 21 hrs/week? Select sample (n = 16) unknown n Nondirectional hypothesis: H 0 : = 21; H 1 : 21 l reject H 0 if increase or decrease n PASW/SPSS: Test value = 21 l Assumed from H 0 ~

PASW One Sample T Test n Menu l Analyze l Compare Means l One-Sample T Test n Dialog box l Test Variable(s) (DV) Test Value (value of testing against) l Options (to change confidence intervals) ~

PASW Output *1-tailed probability: divide Sig. 2-tailed by 2

Paired-Samples t-tests n 2 samples are statistically related l Less affected by individual differences l reduces variance due to error n Repeated-measures l 2 measurements on same individual n Matched-subjects l Match pairs on some variable(s) l Split pairs into 2 groups ~

Difference Scores n Find difference between each score l D = X 2 - X 1 l Requires n 1 scores equal n 2 scores n Calculate mean D l n And standard deviation of D l ~l ~

Repeated-measures n 2 measurements of same individual n Pretest-posttest design l measure each individual twice l pretest treatment posttest l compare scores ~

Matched-subjects n Match individuals on important characteristic l individuals that are related l IQ, GPA, married, etc n Assign to different treatment groups l each group receives different levels of independent variable ~

Assumptions: Related Samples n Population of difference scores is normal n Observations within each treatment independent l scores for each subject in a group is independent of other subjects scores ~

Related-samples Hypotheses n Nondirectional H 0 : D = 0 H 1 : D 0 n Directional H 0 : D > 0 H 1 : D < 0 l Remember: it depends on the direction of the prediction ~

Sample Statistics n Mean difference n Mean for single sample

Standard Deviation: Related-samples Single sample

Estimated Standard Error n Calculate same as single sample l use standard deviation of difference scores

Test Statistic n Related-samples t test Since D = 0

Example n Does exercising longer have greater health benefits? n Participants l 7 pairs of people matched on age, sex, & weight n Manipulation (IV) l 1 of each pair exercised 2 hrs/week l 1 of each pair exercised 5 hrs/week n Outcome (DV): Health rating ~

PASW Paired-Sample T Test n Data entry l 1 column each DV n Menu l Analyze l Compare Means l Paired-Sample T Test n Dialog box l Paired Variable(s) (DV) l Options (to change confidence intervals) ~

PASW Output