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Statistical power is… Statistical power is… …the probability of being able to detect (through statistical significance testing) an effect of a specified magnitude. Scenario • Student 1: So how’s the big “D” going? Scenario • Student 1: So how’s the big “D” going? • Student 2: I just ran the correlation between my two measures. The correlation is .65, but darn it, it’s not significant, and my advisor tells me that I can’t get my degree until I have significant results. Scenario • Student 1: So how’s the big “D” going? • Student 2: I just ran the correlation between my two measures. The correlation is .65, but darn it, it’s not significant, and my advisor tells me that I can’t get my degree until I have significant results. • Student 1: Bummer. You are a loser! Scenario • Student 1: So how’s the big “D” going? • Student 2: I just ran the correlation between my two measures. The correlation is .65, but darn it, it’s not significant, and my advisor tells me that I can’t get my degree until I have significant results. • Student 1: What was your sample size? Scenario • Student 1: So how’s the big “D” going? • Student 2: I just ran the correlation between my two measures. The correlation is .65, but darn it, it’s not significant, and my advisor tells me that I can’t get my degree until I have significant results. • Student 1: What was your sample size? • Student 2: I had 8 subjects. Scenario • Student 1: So how’s the big “D” going? • Student 2: I just ran the correlation between my two measures. The correlation is .65, but darn it, it’s not significant, and my advisor tells me that I can’t get my degree until I have significant results. • Student 1: What was your sample size? • Student 2: I had 8 subjects. • Student 1: You miserable fool! … = d x f (N) = d (N-1) 1/2 = ρ (N-1) 1/2 Graphical Data Displays and Interpretation 2010 November 10 John Tukey (1977), Exploratory Data Analysis. Edward Tufte, The Visual Display of Quantitative Information. John Tukey (1977), Exploratory Data Analysis. Edward Tufte, The Visual Display of Quantitative Information. Tufte Principles of Graphical Excellence Graphical excellence is the well-designed presentation of interesting data -- a matter of substance, of statistics, and of design. Graphical excellence consists of complex ideas communicated with clarity, precision, and efficiency. Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space. Graphical excellence is nearly always multivariate. Graphical excellence requires telling the truth about the data. Figure 6 Reading Comprehension “White space” Age Equivalent Score 12 11 10 9 8 7 6 5 Program 4 3 0 1 2 3 4 GRADE 5 6 Bilingual English-Only Figure 2 English oral proficiency, reading and writing development and redesignation probability from LEP to FEP as a function of grade level. District A. 1.0 Mean Score, 1 = Criterion 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Measure 0.2 0.1 0.0 0 1 2 3 4 GRADE 5 6 7 Redesignation Writing Reading Oral English Increased ELP growth 30 Graphical Excellence Award deadline: NEXT MONDAY • Find an example of graphical excellence that tells a story in a simple, elegant manner. • Or… find a real dog of an example from which we can learn what not to do.