Inferential Stats for Two-Group Designs

Inferential Statistics Used to infer conclusions about the population based on data collected from sample Do the results occur frequently or rarely by chance? Two-group designs: –one control group vs. experimental group –two experimental groups –Two samples representing two populations

Inferential Statistics Null hypothesis: differences between groups are due to chance (i.e., not due to the manipulation of IV). –Results are not significant Results are Significant: results would occur rarely by chance alone. Therefore, likely due to the manipulation of the IV. –p<.05 or p <.01

Single samples t-test Compared single sample with a population –Given population mean –Derived sample mean, standard deviation and standard error of the mean –Conducted t-test –Determined critical t value (one-tailed vs. two-tailed) based on df –Reject H 0 : the sample comes from a population that is different from the comparison population. –Sustain H 0 : the sample and comparison population come from the same population.

T-test (Difference between Means) t-test: Inferential statistical test used to evaluate the difference between two groups or samples. Two types: –t-test for independent samples (between-subjects design) – t-test for paired samples (within-subjects design)

T-test for independent samples Compares means of 2 different samples of participants. Assesses the differences between these 2 samples. Do participants in each sample perform so similarly so that they are likely to come from the same population? Do participants in each sample perform so differently so that they are likely to represent 2 different populations?

Assumptions of independent samples t-test Data are interval-ratio scale Normally distributed (bell shaped) Observations of one group are independent of other group. Homogeneity of variance –Variance: shows spread the scores are from the mean (standard deviation squared) –The variance of 2 populations represented by each sample should be equal.

Independent samples t-test Two groups of 8 salesclerks, each tested only once. IV: dress style of customers levels: –Sloppy Clothing customers –Dressy Clothing customers DV: response time of clerks to help customers

Reaction time (seconds)

Degrees of freedom for independent groups: df = N - 2

Independent samples t-test Formula pg 198 Numerator: difference between 2 sample means Denominator: standard error of the difference between means of independent samples. Rationale: according to H 0, μ1 = μ2, so the difference between population means is zero. –according to H 1, μ1 ≠ μ2, and their difference should be large enough to be significant.

Independent samples t-test Rationale continued: If we took an infinite number of samples from each population, calculated their means, subtracted the means from each other, and plotted the difference, we would get a distribution of differences between sample means. When we take the standard deviation of this new distribution, we get the standard error of the difference between means of independent samples.

Independent samples t-test Steps: –1) calculate means of each sample. –2) calculate the variance of each sample. –3) determine the std error of difference between means. –4) calculate independent samples t-test –5) determine t critical (based on df = N-2; alpha level, one vs two-tailed) –6) make decision: reject or do not reject null hypothesis

Factors that Increase power To increase power in independent samples: –Increase differences between the means (i.e., choose an IV that will produce greater differences between groups) –Reduce variability of raw scores in each condition (variance will be smaller) –Increase sample size

Textbook example pg. 197

Hw problem # 1

Correlated-groups t-test or paired samples t-test One sample where each participant is tested twice (within-subjects design). Measures whether there is a difference in the sample means and if this difference is greater than expected by chance. –H 0 : there is no difference between the scores of person A in condition 1 and condition 2. –H 1 : person A performs differently in condition 1 than condition 2. Determine difference scores: difference between participants’ performance in condition 1 and performance in condition 2.

Correlated-samples t-test Difference scores: pg 204, table 9.3 Formula pg. 204 Numerator: mean of difference scores minus zero Denominator: standard error of difference scores –Standard deviation of the difference scores divided by √N Degrees of freedom: N - 1

Paired-samples t-test textbook pg. 204

Paired samples t-test Steps: –1) calculate the difference scores for each participant. –2) calculate the mean of difference scores. –3) determine the std deviation of difference scores. –4) calculate the std error of the difference scores: divide # 3 by square root of N –5) calculate paired samples t-test –6) determine t critical (based on df = N-1; alpha level, one vs two-tailed) –7) make decision: reject or do not reject null hypothesis

Assumptions of paired samples t-test Data are interval-ratio scale Normally distributed (bell shaped) Observations are correlated; dependent on each other Homogeneity of variance –Variance: shows spread the scores are from the mean (standard deviation squared) –The variance of 2 populations represented by each condition should be equal.

Hw prob. # 3