1. Introduction to Basic Statistical Tools for Research OCED 5443 Interpreting Research in OCED Dr. Ausburn OCED 5443 Interpreting Research in OCED Dr. Ausburn

2. No One Panic! We are not going to calculate anything We are not going to delve into statistical intricacies We are going to see how some important statistics are used and reported in research We are going to focus on how to interpret reported statistics We are going to look carefully at examples of every statistic we talk about We are going to talk it over until you understand

3. Good Data Makes You a…. Research Star!

4. Descriptive Statistics (Non- Inferential) Summary Snapshot of Sample Measures of Central Tendency (How Data “Clusters”) Mean (X) – Group’s Arithmetic “average” Mode (Mo) – Number appearing most frequently in group Median (Md) – Point that splits the group in half; the group’s midpoint

5. Descriptive Statistics (Non- Inferential) Summary Snapshot of Sample Measures of Dispersion (How Data “Spreads”) Range – Difference between highest point and lowest point in group –Exclusive (high – low) –Inclusive (high – low + 1) Quartile Deviation (Semi-Interquartile Range) – Spread off the Median Variance (s 2 ) – Spread off the Mean –Based on “deviation scores” (score – mean of scores) –Deviation score = deviation of score from the mean –Variance represents random (“error”) variation of scores within a group –Used in many inferential statistics Standard Deviation (s or sd) – Spread off the Mean –Positive square root of the variance –Sort of an “average” deviation from the Mean –Important statistically due to relationship to Mean and Normal Distribution Curve

6. Descriptive Statistics (Non- Inferential) Summary Snapshot of Sample Measure of Distribution (How Data is Grouped) Frequency distribution –Usually presented in a frequency table or graph –Data divided into categories –Number of people in group who fall into each category = “frequency” (ƒ)

7. Descriptive Statistics (Non- Inferential) Summary Snapshot of Sample Measures of Relationship (How Variables Rise and Fall Together) Correlation Coefficients (r, r xxx, R) –Numerous types; choice depends on types of data being correlated –Requires 2 sets of data on 1 group of people; 2 measures on same people –Values between 0 and 1; may be positive or negative –Strength/Magnitude = how close to 1 –Direction = + or – –Shows only relationship: How the 2 variables “vary together” –Does NOT imply causality, much less direction of causality!

8. Descriptive Statistics (Non- Inferential) Summary Snapshot of POPULATION Describing a Population is just like describing a Sample Measures of Central Tendency (pop. Mean=  ) Measures of Dispersion (pop. variance/sd =  and  2 ) Frequency Distributions Correlation Coefficients A measure on a sample is called a statistic A measure on a population is called a parameter

9. Inferential Statistics Tests of significance Hypothesis testing Infer from sample to population Comparisons of Frequency Distributions Chi-Square (  2 ) Tests - Several variations - Data must be in frequencies (ƒ) - Compare “observed” ƒs to “expected” ƒs

10. Chi-Square Tests: Interpreting the “Answer”  2 = value of chi-square df = degrees of freedom for the test will be listed p = or p  = or  (or % level) %, probability or alpha level will be listed Interpretation? Let’s look at example and see what this all means

11. Inferential Statistics Testing and Predicting Relationships among Variables Correlation coefficients –Same types and rules used for descriptive purposes –Remember: Correlation does not imply causality Regression analysis –Linear regression –Multiple regression Cluster analysis Factor analysis Tests of significance Hypothesis testing Infer from sample to population

12. Inferential Statistics Testing Means for Significant Differences t-test (or “student’s t”) Analysis of Variance (ANOVA) or F-test Variations on ANOVA for special circumstances Non-parametric versions for some samples that won’t meet assumptions of t and F Tests of significance Hypothesis testing Infer from sample to population

13. Inferential Statistics Must have only: –1 independent variable –2 groups separated on the independent variable –1 dependent variable Thus: 2 groups compared on 1 score or measurement Several versions of t-test for use in various circumstances –Independent t (groups not related) –Correlated t (groups related or “repeated measures”) –Unpooled variance (most samples) –Pooled variance (small samples) Tests of significance Hypothesis testing Infer from sample to population The t-Test

14. Inferential Statistics The t -Test t-Test examines 2 group means to see if they are “significantly” different The “significant” refers to statistical significance only Uses variance within and between groups to compare the means (Remember, variance is related to distance of scores from the group mean) To have a “significant” t-value, variance between groups must be greater than variance within groups by a critical amount Tests of significance Hypothesis testing Infer from sample to population

15. t-Tests: Interpreting the “Answer” t = value of t will be reported df = degrees of freedom for the test will be listed p = or p  = or  (or % level) %, probability or alpha level will be listed Interpretation? Let’s look at example and see what this all means

16. Inferential Statistics ANOVA (F test) Must have: –1 or more independent variables (“Factors”) –2 or more groups separated on the independent variable(s) –1 dependent variable –For more than 1 dependent variable, run series of ANOVAs or a MANOVA Compare to t-Test requirements Several variations of ANOVA family, including: –One-way ANOVA –Factorial ANOVA –MANOVA (Multiple ANOVA) –ANCOVA (Analysis of Co-Variance) To get a “significant” F, variance between groups must exceed variance within groups by a critical amount F is actually a ratio of variance between to variance within Within-group variance is “error” variable Tests of significance Hypothesis testing Infer from sample to population

17. Inferential Statistics One-Way ANOVA Must have –1 Factor (independent variable) –2 or more groups to compare –Groups are separated on the identified factor –1 dependent variable –For more than 1 dependent variable, run series of ANOVAs or a MANOVA One-way ANOVA with 1 Factor and only 2 goups = t-Test –t 2 = F –Can use either test –t is usual choice in this case 1-way ANOVA must be used for 1 Factor and more than 2 groups Tests of significance Hypothesis testing Infer from sample to population

18. 1-way ANOVA: Interpreting the “Answer” F = value of F will be reported df = 2 degrees of freedom for the test will be listed df within and df between (F 2,36 ) p = or p  = or  (or % level) %, probability or alpha level will be listed Interpretation? Let’s look at example and see what this all means

19. Inferential Statistics Factorial ANOVA Must have –2 or more Factors (independent variable) –2 or more groups to compare –Groups are separated on the identified factors –1 dependent variable –For more than 1 dependent variable, run series of ANOVAs or a MANOVA Each Factor may have 2 or more variations or “levels” Factorial ANOVA with only 2 factors are usually called “2-way ANOVAs” Tests of significance Hypothesis testing Infer from sample to population Let’s look at some examples Note difference between: - Factors - Levels - Cells

20. Factorial ANOVA: Interpreting the “Answer” F = multiple values of F will be reported: (a) an F for “main effect” for each Factor (b) an F for “interaction” of the factors df = degrees of freedom for each F will be listed p = or p  = or  (or % level) %, probability or alpha level will be listed for each F Interpretation? Let’s look at example and see what this all means

21. Post-Hoc Tests with ANOVA Interpretation? Let’s look at example and see what this all means “After the fact” tests – done after ANOVA in certain conditions –When have more than 2 groups –When find significant F with more than 2 groups Done to locate exactly where the significant F occurs 2 common tests – each used under certain circumstances –Tukey test (T-method) –Scheffe tests (S-method)

22. Introduction to Basic Statistical Tools for Research Questions and Discussion