How To Design and Evaluate Research in Education Chapter 10: Descriptive Statistics

1. How To Design and Evaluate Research in EducationChapter 10: Descriptive Statistics Sherry Alessandro Susan Ray

2. Permits researchers to succinctly describe information Uses few indices Uses indices to calculate data for a SAMPLE Uses two (2) types of numerical data: Quantitative data Categorical data Descriptive Statistics: Defined Sample Total Population

3. Quantitative Data • Variable measured along a scale • Scale indicates how much of the variable is present • Reported in scores • Higher score = more of the variable presence (example: knowledge of algebra)

4. Categorical Data • Represents total number of objects, people, or events researcher finds in a category • Researcher looks for frequency • Converts frequency to percentages

5. Techniques Used to Summarize Quantitative Data • Polygons: • Frequency – summarizes data for one variable • Skewed – lopsidedness • of distribution • Positive • Negative • Curves: smoothing the angles in polygons

6. Measures of Central Tendency(Single number summary of distribution) • Mode - most frequent score • Median – 50% below, 50% above • Mean – average

7. Spread/Variability(how far from the center the data range) • Interquartile range (divide data into 4 groups & see how far apart the extreme groups are) percentile • 25th, 50th (median), 75th • 5 number summary • Boxplot = visual representation of 5 number summary • Overall range – highest minus lowest • Standard deviation – most useful – represents the spread from the mean in a distribution

8. Standard Deviation • Represents all scores in distribution • Mean, median & mode are the same • Mean is at the center of curve

9. Standard Scores • Scale to show one individual compared to others in a group • z scores: # of standard deviation units of raw score from the mean (1 z = 1 SD) compare raw scores on different tests • Probability – odds of event occurring

10. Standard Scores continued • T scores – z scores by any other name! • Z score X 10 + 50 • Normalized distribution of scores- when scores do not form a normal curve • Assumes that characteristic is “really” normally distributed

11. Standard Score Examples

12. Correlation • Relationship between two or more variables such as: • Age and weight • S.A.T. scores & college performance • Does not prove causation • Perfect positive correlation = +1.00 • Perfect negative correlation = -1.00 Age: 45 Age: 8 Wt.: 190# Wt: 56#

13. Scatterplots (Outlier) • Useful technique for showing the degree of relationships • Pictorial representation of relationship between two quantitative variables College Achievement High Low Low High SAT Scores

14. Pearson Product-Moment Coefficient Over eat/ Lose Weight Over eat/Gain Weight Over eat/ Drive Safely

15. Techniques for Summarizing Categorical Data • Frequency Tables show breakdown of survey responses (or any data sets) and percentages Response Tally Frequency % Yes 8 40 No 5 25 Don’t Know 4 20 Don’t Care 3 15 n = 20 100 %

16. Pie & Bar Graphs • Visual representation of data

17. Crossbreak Tables(aka Contingency Tables) • Visual of comparative data • Simple to “see” and extract data • Often used to analyze data from new perspectives

18. Positive & Negative Correlations “An apple a day keeps the doctor away” implies a NEGATIVE correlation between apple eating and illness. “Idle hands are the devil’s workplace” Implies a POSITIVE correlation between idleness and mischief.

19. Closing Points • Statistics describe characteristics of a sample • Data summarized numerically or graphically