The slides touche briefly statistical procedures employed for interpreting test results. The file is especially useful for ESL teachers

1. Kinds of Statistics Purpose Target Characteristics Descriptive Statistics Summarizing, Describing Sample Statistic Inferential Statistics Analyzing, Generalization Population Parameter

4. Tabulation of Data Ungrouped Data Grouped Data 15 9 16 13 11 10 8 12 16 15 13 12 11 10 9 8

7. Frequency distribution Score (X) Absolute Frequency Relative Frequency 16 15 13 12 11 10 9 8 1 1 2 5 4 4 1 2 0.05 0.05 0.10 0.25 0.20 0.20 0.05 0.10 Σ x = 94 N= 20 1.00

8. Frequency distribution Score (X) Absolute Frequency Relative Frequency Percentage 16 15 13 12 11 10 9 8 1 1 2 5 4 4 1 2 0.05 0.05 0.10 0.25 0.20 0.20 0.05 0.10 0.05x100=5 0.05x100=5 0.10x100=10 0.25x100=25 0.20x100=20 0.20x100=20 0.05x100=5 0.10x100=10 Σ x = 94 N= 20 1.00 100

20. Example Σ x 2 28 (V ( = ---------= --------=4.6 N-1 7-1  S = 2.14 X (X - ) Σ (X - ) 2 19 18 17 16 15 14 13 + 3 +2 +1 0 -1 -2 -3 9 4 1 0 1 4 9 112 0 28

40. Perfect Correlation

41. Correlation Coefficient - Interpretation

43. Correlation Coefficient - Formula

49. As another example, where the whole-test mean for Ss answering correctly is 30; the whole-test mean for Ss answering incorrectly is 45; the standard deviation for the whole test is still 8.29; the proportion of Ss answering correctly is still .50; and the proportion answering incorrectly is still .50 .

50. Types of Correlation coefficients Type of Correlation Coefficient Types of Scales Pearson product-moment Both scales interval (or ratio) Spearman rank-order Both scales ordinal Phi Both scales are naturally dichotomous (nominal) Biserial One scale artificially dichotomous (nominal), one scale interval (or ratio) Point-biserial One scale naturally dichotomous (nominal), one scale interval (or ratio) Gamma One scale nominal, one scale ordinal