1. Statistical Fundamentals: Using Microsoft Excel for Univariate and Bivariate Analysis Alfred P. Rovai One-Sample t-Test PowerPoint Prepared by Alfred P. Rovai Presentation © 2015 by Alfred P. Rovai Microsoft® Excel® Screen Prints Courtesy of Microsoft Corporation.

2. One-Sample t-Test Copyright 2015 by Alfred P. Rovai The one-sample t-test, also known as the single-sample t-test, is a parametric procedure that compares a calculated sample mean to a known population mean or a previously reported value in order to determine if the difference is statistically significant. For example, an educational researcher might want to determine if the mean sense of classroom community score among university students enrolled in fully online programs differs significantly from the hypothesized population score of 30. Excel data entry for the one-sample t-test is accomplished by entering the value for each case of the variable of interest in a single column of an Excel spreadsheet.

3. One-Sample t-Test Copyright 2015 by Alfred P. Rovai One can compute the t-value using the following formula: where the numerator is the difference in group means and the test value and the denominator is the estimated standard error of the sample divided by the square root of the sample size.

4. One-Sample t-Test Copyright 2015 by Alfred P. Rovai Cohen’s d measures effect size and is often used to report effect size following a significant t-test. The formula for Cohen’s d for the one-sample t-test is: By convention, Cohen’s d values are interpreted as follows: – Small effect size =.20 – Medium effect size =.50 – Large effect size =.80

5. Key Assumptions & Requirements Copyright 2015 by Alfred P. Rovai Random selection of samples to allow for generalization of results to a target population. Variables. One continuous dependent variable (DV) measured on the interval or ratio scale. Independence of observations. observations (i.e., measurements) are not acted on by an outside influence common to two or more measurements. Normality. One DV normally distributed. Sample size. The one-sample t-test is robust to minor violations of the assumption of normally distributed data with sample sizes > 30.

6. Copyright 2015 by Alfred P. Rovai TASK Respond to the following research question and null hypothesis: Is there a difference in the mean sense of classroom community (c_community) score among university students enrolled in fully online programs and the norm of 30, μ ≠ 30? H 0 : There is no difference in the mean sense of classroom community score of university students enrolled in fully online programs and the norm of 30, μ = 30. Open the dataset Motivation.xlsx. Click on the One-Sample t-Test worksheet tab. File available at http://www.watertreepress.com/stats http://www.watertreepress.com/stats Conducting the One-Sample t-Test

7. Copyright 2015 by Alfred P. Rovai Go to the One-Sample t-Test tab of the Motivation 3rdEd.xlsx Excel workbook. Enter the labels and formulas shown in cells B1:C13. Note: cell C4 contains the test value from the null hypothesis.

8. Copyright 2015 by Alfred P. Rovai Test results provide evidence that there is sufficient evidence (p = 0.02) to reject the null hypothesis that there is no difference in the mean sense of classroom community score of university students enrolled in fully online programs and the norm of 30. Test Results Summary

9. Copyright 2015 by Alfred P. Rovai As a minimum, the following information should be reported in the results section of any research report: null hypothesis that is being evaluated to include test value, descriptive statistics (e.g., M, SD, N), statistical test used (i.e., one-sample t- test), results of evaluation of test assumptions, as appropriate, and test results. For example, one might report test results as follows. The formatting of the statistics in this example follows the guidelines provided in the Publication Manual of the American Psychological Association (APA). Results A one-sample t-test was conducted to evaluate the null hypothesis that there is no difference in the mean sense of classroom community score of university students enrolled in fully online programs and the norm of 30 (N = 169). The test showed that the sample mean (M = 28.84, SD = 6.24) was significantly different than the test value of 30, t(168) = 2.42, p =.02 (2-tailed), d =.19. Consequently, there was sufficient evidence to reject the null hypothesis. Reporting One-Sample t-Test Results

10. Copyright 2015 by Alfred P. Rovai One- Sample t- Test End of Presentation