1. Statistical Fundamentals: Using Microsoft Excel for Univariate and Bivariate Analysis Alfred P. Rovai Hypothesis Testing PowerPoint Prepared by Alfred P. Rovai Presentation © 2013 by Alfred P. Rovai Microsoft® Excel® Screen Prints Courtesy of Microsoft Corporation.

2. Copyright 2013 by Alfred P. Rovai Hypothesis Testing A hypothesis test is a statistical method used to reach a conclusion that extends beyond the sample measured to a target population. To determine the accuracy of a conclusion with 100% accuracy requires examination of an entire population (i.e., a census). This is often not feasible for large populations, e.g., all undergraduate university students in the state of Virginia or all workers who abuse drugs, because of time and cost considerations. Instead, a sample is drawn from the target population, the sample is measured and analyzed, a conclusion is reached regarding the sample, and the conclusion is extended to the population. There is always a chance of error because the entire population was not examined.

3. Sampling Copyright 2013 by Alfred P. Rovai Identify the target population Obtain a list of the target population (sampling frame) Identify a method for selecting units from the sampling frame that is representative of the target population Determine the sample sizeConduct the sampling

4. Identify Statistical Hypotheses Copyright 2013 by Alfred P. Rovai Research Hypothesis (H1 or HA) Related to the research question; the outcome that the researcher desired or expected For example, H 1 : There is a difference in mean computer confidence posttest between male and female university students, μ1 ≠ μ2 Null Hypothesis (H0) Opposite of the research hypothesis; maintains the status quo; no difference or relationship For example, H o : There is no difference in mean computer confidence posttest between male and female university students, μ1 = μ2

5. Copyright 2013 by Alfred P. Rovai Purposes of Hypotheses Link theory with the problem statement Enable the researcher to objectively enter areas of discovery Provide direction to the research by identifying the expected outcome

6. Copyright 2013 by Alfred P. Rovai Research Hypothesis Literature Review Theoretical Framework Problem Statement Important Interrelationships

7. Reaching a Statistical Conclusion Copyright 2013 by Alfred P. Rovai 1 Statistical hypotheses are stated (H0 and H1) 2 Ho is tested using an appropriate hypothesis test 3 Ho is considered true unless the statistical evidence suggests that it is false. If false, one concludes that there is evidence to reject H o and accept the research hypothesis.

8. One- and Two-Tailed Hypotheses Copyright 2013 by Alfred P. Rovai One-Tailed Hypothesis Hypothesis is directional, e.g., Ho: Male university students have a greater computer confidence posttest mean than female university students, μMales > μ Females. The test determines whether or not the mean of a specified group is greater than the mean of the other group. Two-Tailed Hypothesis Hypothesis is nondirectional, e.g., Ho: There is no difference in mean computer confidence posttest between male and female university students, μMales = μ Females. The hypothesis test determines whether or not the mean of one group is either less than or greater than the mean of the second group. Many researchers believe that two-tailed tests should always be used, even when making directional predictions.

9. Key Points Copyright 2013 by Alfred P. Rovai A statistical hypothesis ALWAYS refers to the population, not the sample that is measured. It ALWAYS refers to a parameter, e.g., μ, and never a statistic, e.g., M A hypothesis test ALWAYS starts by assuming Ho is true The purpose of the hypothesis test is to seek evidence that supports rejecting Ho and accepting H1 A statistically significant hypothesis test occurs when there is statistical evidence to reject Ho NEVER conclude Ho is true since there is always a chance of error. Rather, conclude, if warranted, that there is insufficient evidence to reject Ho

10. Choose a Significance Level Copyright 2013 by Alfred P. Rovai The significance level is the probability of making a Type I error (α); that is, falsely rejecting a true Ho An à priori value significance level is determined before one conducts any hypothesis test This value is typically set at.05 for social science research and becomes the standard for rejecting or failing to reject Ho A significance level of.05 means that one is willing to accept an error of no more than 5 out of 100 in rejecting H o Analysis of sample data results in a p-value (probability value); that is, the probability of falsely rejecting the true Ho If the p-value > the à priori significance level there is insufficient evidence to reject Ho If the p-value <= the à priori significance level there is sufficient evidence to reject Ho

11. Statistical Power of a Test Copyright 2013 by Alfred P. Rovai Statistical power (or observed power or sensitivity) of a statistical test is the probability of rejecting a false H 0. -Equals 1 minus the probability of accepting a false H 0 (1 – β). -Represents the degree one is willing to make a Type II error. The desired standard is 80 percent or higher, leaving a 20 percent chance, or less, of error.

12. Statistical Decisions Copyright 2013 by Alfred P. Rovai Ho is True Reject Ho: Type I error (α) Fail to Reject Ho: No Error (1 – α) Ho is False Reject Ho: No Error (1 – β) Fail to Reject Ho: Type II Error: (β)

13. Decision Errors Copyright 2013 by Alfred P. Rovai Setting a more liberal à priori significance level, e.g., α =.10 - Increases the probability of a Type I error. - Decreases the probability of a Type II error. Setting a more conservative à priori significance level, e.g., α =.001 - Decreases the probability of a Type I error. - Increases the probability of a Type II error.

14. Statistical Significance Copyright 2013 by Alfred P. Rovai Statistical significance does not imply an effect is meaningful or important. While statistical significance is concerned with whether a statistical result is due to chance, practical significance is concerned with whether the result is useful in the real world. Effect size is a measure of the magnitude of a treatment effect and is used to assess practical significance. There is no practical significance without statistical significance. Effect size is the degree to which H0 is false. Effect size can be measured in one of several ways.

15. Two Common Effect Size Measures Copyright 2013 by Alfred P. Rovai Cohen’s d (standardized difference between two means). Small, d =.20Medium, d =.50Large, d =.80 Pearson r (correlation coefficient between two continuous variables). Between 0 and ±0.20 – Very weak Between ±0.20 and ±0.40 – Weak Between ±0.40 and ±0.60 – Moderate Between ±0.60 and ±0.80 – Strong Between ±0.80 and ±1.00 – Very strong Note: other interpretive guides exist in the professional literature.

16. Methods of Increasing Statistical Power Copyright 2013 by Alfred P. Rovai Increase the sample size Increase the significance level, e.g.,.05 to.10 Use all the information provided by the data, e.g., do not transform interval scale variables to ordinal scale variables Use a one-tailed versus a two-tailed test Use a parametric versus nonparametric test

17. Hypothesis Testing Steps Copyright 2013 by Alfred P. Rovai 1 Restate the research question as Ho and H1 2 Decide on the à priori significance level 3 Choose an appropriate hypothesis test 4 Select & measure a sample from the target population 5 Conduct the hypothesis test and state a conclusion 6 Communicate the findings and implications for practice

18. Statistical Conclusion Copyright 2013 by Alfred P. Rovai Every hypothesis test will result in one of two conclusions: There is sufficient evidence to reject H 0 There is insufficient evidence to reject H 0 NEVER accept H0 since there is always a chance of error

19. Research Conclusion Copyright 2013 by Alfred P. Rovai The conclusion reached by hypothesis test must also be expressed in terms of the research problem and implications for practice.

20. Hypothesis Testing End of Presentation Copyright 2013 by Alfred P. Rovai