Comparing Two Means Onesample Pairedsample ttests Lesson 13

Comparing Two Means: One-sample & Paired-sample t-tests Lesson 13

Inferential Statistics 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 ~ n

Comparing 2 means: t-tests 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 ~ n

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

t statistic

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

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

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

Paired-Samples t-tests 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 ~ n

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

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

Matched-subjects 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 ~ n

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

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 l Since m. D= 0

Example Is arachnophobia limited to real spiders or is a picture enough? n Participants l 12 spider phobic individuals n Manipulation (IV) l Each person exposed to a real spider & picture of same spider at two different times n Outcome (DV): Anxiety n

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

PASW Output

Reporting the Results n On average, participants experienced significantly greater anxiety to real spiders (M = 47. 00, SE = 3. 18) than to pictures of spiders (M = 40. 00, SE = 2. 68), t(11) = − 2. 47, p <. 05