CHAPTER 15: THE NUTS AND BOLTS OF USING STATISTICS

Using Statistics Hypothesis testing  Hypothesis tests are designed to look for evidence against the null hypothesis that predicts no difference between conditions or no relationship between variables, depending on what type of research question a study is designed to answer.  If our calculated statistic falls in the most extreme portion of this distribution, called the critical region, we have enough evidence to reject the null hypothesis and accept the scientific/alternative hypothesis that there is a difference or relationship. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Using Statistics McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Groups or Conditions A significant difference between groups or conditions allows researchers to conclude that an effect exists in the population because they are able to reject the null hypothesis in a significant test. Sample mean differences can be caused by the effect, by sampling error, or both. A larger statistical value indicates a larger treatment effect because it represents the sample mean difference due just to the effect. Larger statistical values also lead to more power to detect effects with the test. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Groups or Conditions The chance of obtaining a statistical value when the null hypothesis is true is determined to look for evidence against the null hypothesis. The distribution of statistical values when the null hypothesis is true is used to determine the p-value for the value calculated in the test. If the p-value for the statistic is less than or equal to the alpha level, the null hypothesis is rejected, and the researcher concludes that there is an effect. If the p-value is greater than the alpha level, the researcher cannot reject the null hypothesis and must conclude that there is no evidence of an effect. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Two Means with t-Tests One-sample t-test  is often used when the population mean without a treatment is known and is being compared with a sample mean that represents the population with a treatment. Population means are known for certain types of variables, such as standardized tests that have been given to many samples in the past or were designed to have a specific population mean. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Two Means with t-Tests Independent samples t-test  is used when two samples of different individuals are compared. Each sample represents the population for that group or condition. Thus, there are two sample means that are compared in the test. For example, if researchers are interested in differences in depression scores between men and women, they would collect a sample of men and a sample of women and compare the two sample means for depression scores. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Two Means with t-Tests Paired/related samples t-test  is used if two related samples (e.g., each individual in one sample is matched with one individual in the other sample on some characteristic) or two sets of scores from the same individual (i.e., the individual provides scores in more than one condition) are compared. If two sample means are related from matched individuals or the same individual, the variability is likely to be lower, and an effect is more likely to be detected (i.e., the test will have more power) than if the samples are independent. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Two Means with t-Tests Paired/related samples t-test  is used if two related samples (e.g., each individual in one sample is matched with one individual in the other sample on some characteristic) or two sets of scores from the same individual (i.e., the individual provides scores in more than one condition) are compared. If two sample means are related from matched individuals or the same individual, the variability is likely to be lower, and an effect is more likely to be detected (i.e., the test will have more power) than if the samples are independent. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing Two Means with t-Tests McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Using SPSS to Conduct t-Tests When researchers conduct inferential statistics tests, they rarely conduct the tests with hand calculations. Most researchers use a statistical software package, such as SPSS, to conduct the tests. The software package takes the raw data the researcher inputs, calculates descriptive statistics, and conducts significance tests that the researcher specifies. The output typically includes descriptive values (e.g., means, standard deviations), the value of the test statistic calculated (e.g., t, F, r) and the p-value associated with the statistical value calculated. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Using SPSS to Conduct t Tests One-sample t-test Independent samples t-test Paired samples t-test McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Comparing More Than Two Means with ANOVA Analysis of variance (ANOVA) is used to test an effect when more than two groups or conditions are being considered. An F-statistic is calculated for each effect tested based on the ratio of average variance between the condition means and the average variance within the conditions. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

The comparison of means for each level of an independent (or quasi-independent) variable is called the main effect. If a main effect is significant in an ANOVA, it indicates that there is a mean difference somewhere among the means tested. The main effect does not tell you which means are different from one another. You must conduct additional tests, called post hoc tests, to determine which means are different. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc. Comparing More Than Two Means with ANOVA

An interaction effect is also tested in an ANOVA for all combinations of independent variables. The interaction effect tests the effect of one independent variable at each level of the other variable. The interaction effect is tested by comparing the difference in condition means across levels of one independent variable for each level of the other independent variable(s). McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc. Comparing More Than Two Means with ANOVA

Using SPSS to Conduct ANOVAs Between-subjects design Within-subjects design Factorial ANOVA McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Looking for Relationships with Pearson r & Regression Tests Chi-square test: a significance test used to determine if a relationship exists between two variables measured on nominal or ordinal scales. Pearson r test: a significance test used to determine if a linear relationship exists between two variables measured on interval or ratio scales. Linear regression: a statistical technique that determines the best fit line to a set of data to allow prediction of the score on one variable from the score on another variable. McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.

Using SPSS with Pearson r & Regression Chi-square analyses Pearson r test Simple linear regression McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.