Chapter 11: Test for Comparing Group Means: Part I

Learning Objectives Understand approaches to difference testing to answer a proposed research question Evaluate assumptions of difference tests Distinguish independent sample difference test from dependent sample difference test Understand the purpose of multiple comparison testing

Learning Objectives (Cont’d) Distinguish how the number of groups influences the choice of statistical test of difference Report the necessary findings in APA style correctly Understand how tests of differences are used in evidence-based practice

Introduction Tests of differences of means are usually used to make comparisons. e.g. how cancer incidence varies depending on sex or gender? Testing the statistical significance between means are also applied to experimental questions e.g. On average, which wound care treatment reduces healing time the most?

Choosing the right test Depends upon the proposed research questions and consideration of factors such as: – the number of groups that will be compared – Whether the groups are independent or dependent

One-sample t-test The simplest t-test where it compares the mean scores of a sample on a continuous dependent variable to a known value e.g. comparing the mean IQ of a sample of students from the university to a known average IQ for the university

One-sample t-test: Assumptions The population mean should be known. The sample should be randomly taken from the population and the subjects within the sample should be independent of each other. Dependent variable should be continuous and normally distributed.

One-sample t-test Hypothesis Statistics

One-sample t-test When p value is less than a chosen alpha, the sample mean is said to be different than 120. When p value is greater than a chosen alpha, the sample mean is said to be not different than 120.

Reporting one-sample t-test Nursing students of the current cohort at ABC university had significantly higher IQ scores (M = , SE = 1.49) than did ABC university students in general, t (99) = 3.42, p <.01, d =.34.

T-test for independent groups Group comparison test for two independent groups T statistic – the difference between means divided by an estimate of the standard error of the difference between those two independent sample means.

T-test for independent groups: Assumptions Sampling distribution should be normal Data should be measured at least an interval level Variances in each groups should be about the same. Measurements should be independent

T-test hypothesis for independent groups Hypothesis

T-test hypothesis for independent groups Statistics

Decision-making using T-test for independent groups When p value is less than a chosen alpha, two group means are said to be the different. When p value is greater than a chosen alpha, two group means are said to be the same.

Reporting T-test results for independent groups On average, the number of beds in Illinois nursing homes (M = 23.8, SE = 4.06) was not significantly different from the number of beds in Ohio nursing homes (M = 34.2, SE = 4.01), t (18) = -1.83, p =.09, r =.40.

T-test for dependent groups Group comparison test for two dependent groups Assumptions – the normality of sampling distribution – data being measured at the interval level

Hypothesis testing for T-test for dependent groups Hypotheses

Hypothesis testing for T-test for dependent groups Statistics

Decision-making for T-test for independent groups When p value is less than a chosen alpha, two group means are said to be the different. When p value is greater than a chosen alpha, two group means are said to be the same.

Reporting T-test results for independent groups On average, the sodium content level after a new diet (M = 145.6, SE = 2.45) was significantly lower than that before a new diet (M = 139.0, SE = 2.41), t (9) = 5.44, p<.001, r =.88.

Analysis of Variance (ANOVA) Group comparison test for more than two independent groups Potentially, one can run multiple t-tests. However, this leads to the inflation of Type I error. – To correct, Bonferroni’s alpha adjustment needed – This does not capture the overall difference across groups.

ANOVA Assumptions – Sampling distribution should be normal – Data should be measured at least an interval level – Variances in each groups should be about the same. – Measurements should be independent

ANOVA Hypothesis Statistics

Decision-making in ANOVA When p value is less than a chosen alpha, group means are said to be the different. – Note that this only indicate that there are at least two group means that differ, not which group differ from which group. – Need to conduct follow-up tests Planned contrast Post hoc When p value is greater than a chosen alpha, group means are said to be the same.

Reporting ANOVA results There was a significant effect of the amount of exercise per week on health problem index, F (3, 76) =12.64, p <.05, ω =.24. Planned contrasts indicated that exercising three days or more per week significantly decreases the number of health problems than exercising less than three days per week, t(76) = -2.24, p<.05, r =.06. A Bonferroni post hoc test indicates that there was a significant difference on the health problem index between the group who do not exercise and the group who exercises five days per week, p =.05. The group who do not exercise had a higher problem index (M = 5.49, SD = 6.03) than the group who exercises five days per week (M = 1.60, SD =1.05).