EDLD 6392 Advanced Topics in Statistical Reasoning Texas A&M University-Kingsville

1. EDLD 6392Advanced Topics in Statistical ReasoningTexas A&M University-Kingsville Research Designs and Statistical Procedures

2. Research Designs by Purpose • Educational Research is conducted for four primary purposes: 1-Description 2-Prediction 3-Improvement 4-Explanation

3. Research Designs by Similarities Experimental & Quasi-experimental -Involves Researcher Intervention Non-experimental - Examines phenomena as they exist Descriptive, Causal-Comparative, and Correlational

4. Descriptive Research Designs The Purpose The description of natural or man-made phenomena-their form, actions, changes over time, and similarities-with other phenomena, an effort to describe. Involves making careful descriptions of educational phenomena, viewed as understanding what people or things mean. Studies primarily concerned with determining “what is.”

5. Descriptive Research (Cont’d) Types of Measurements standardized achievement scores, classroom observation instruments, attitude scales, questionnaires, and interviews Statistics Central Tendency (mean, median, mode) Measures of Variability (SD, variance, range)

6. Causal-Comparative Research The Purpose Purpose of explaining educational phenomena through the study of cause-and-effect relationships. The presumed cause is called the independent variable and the presumed effect is called the dependent variable. Designs where the researcher does not manipulate the independent variable are called ex post facto research.

7. Causal-Comparative (Cont’d) Causal-Comparative research is also a type of non-experimental investigation in which researchers seek to identify cause-effect relationships by forming groups of individuals in whom the independent variable is present or absent and than determining whether the groups differ on the dependent variable.

8. Quasi-Experimental Research Parametric Tests Statistical Analysis: The t Test For testing the significance of difference between two sample means Basic Assumptions 1-Scores form an interval or ratio scale 2-Scores are normally distributed 3-Score variances for the populations under study are equal (SD=SD)

9. Quasi-Experimental (Cont’d) Analysis of Variance (ANOVA) Comparison of two or more group means Multivariate Analysis of Variance (MANOVA) Statistical technique for determining whether groups differ on more than one dependent variable. Basic Assumptions 1-Scores form an interval or ratio scale 2-Scores are normally distributed 3-Score variances for the populations under study are equal (SD=SD)

10. Quasi-Experimental (Cont’d) Nonparametric Tests Nonparametric statistics tests statistical significance that do not rely on any assumptions about shape or variance of population scores. Used with measures that yield categorical or rank scores, or do not have equal intervals. Nonparametric tests are less powerful, they require larger samples to yield the same level statistical significance. 1-The Chi-Square Test = used to determine whether research data in the form of frequency counts are distributed differently for different samples.

11. Quasi-Experimental (Cont’d) Nonparametric Tests (Cont’d) 2-The Mann-Whitney U test=used to determine whether the distributions of scores of two independent samples differ significantly from each other. 3-The Wilcox signed rank test=used to determine whether the distributions of scores of two samples differ significantly from each other when the scores of the samples are correlated.

12. Quasi-Experimental (Cont’d) Nonparametric Tests (Cont’d) 4-The Kruskal-Wallis test=If more than two groups of subjects are to be compared, a nonparametric one-way analysis of variance (Kruskal-Wallis) can be used.

13. Classification of Research Design (Causal-Comparative) O1 X O2 One-group pretest-posttest design Group 1: O1 X O2 Nonequivalent control group Group 2: O3 O4 X1 O1 X2 O2 Equivalent time-samples design

14. Non-experimental Research:Correlational Designs The Purpose To discover relationships between variables through the use of correlational statistics. Involves correlating data on two or more variables for each individual in a sample and computing a correlation coefficient. Two major purposes: 1-To explore causal relationships between variables; 2-To predict scores on one variable from research participants’ scores on other variables.

15. Correlation Research Design Advantages 1-Enables researchers to analyze the relationships among a large number of variables in a single study. 2-They provide information concerning the degree of the relationship between the variables being studied. Parametric Test Pearson r statistical procedure Basic Assumptions 1-Scores form an interval or ratio scale 2-Scores are normally distributed 3-Score variances for the populations under study are equal (SD=SD)

16. Scattergrams Representing Different Degrees and Directions of Correlation between Two Variables Positive correlation (r=.99) Negative correlation (r=-.73) Grade point I.Q. Age gpa Computeruse

17. Choosing Statistical Procedures START Interval Data Relate Compare Not Normal Normal =SD =SD Spearman Correlation Pearson Correlation Dependent Independent 2 groups >2 groups 2 groups >2 groups Mann-Whitney Wilcoxon Friedman ANOVA Kruskal-Wallis Dependent Independent 2 groups >2 groups 2 groups >2 groups Independent Samples t Test ANOVA Related Samples t-Test Repeated Measures ANOVA