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Statistics Statistics • Types • Methods of organizing • Descriptive statistics and analyzing • Definition quantitative data – Central tendency, variability, etc. • Inferential statistics – Chi-squares, t-tests, F-ratios, etc. Descriptive Statistics • Measurement scales – – – – Nominal (male/female, yes/no) Ordinal (high to low) Interval(1, 2, 3. . .) Ratio Visual Depictions of Data • Frequency distributions • Histograms and Bar Graphs Visual Depictions of Data 90 80 70 60 50 40 30 20 10 0 First graders Second graders Third graders 1st Qtr 2nd 3rd Qtr 4th Qtr Qtr Measures of Central Tendency • Mean • Median • Mode Measures of Central Tendency • Normal distribution • Skewed distributions A B C Measures of Variability • How spread out the distribution of scores is from the mean of the distribution • Range • Standard deviation • Percentile Rank • Standard Scores 34.13% 34.13% 2.14% 13.59% 13.59% 2.14% .13% .13% -3 -2 -1 0 +1 +2 +3 Descriptive Statistics • Measures of relationship – Correlation coefficient • High (.70 or above) Moderate (.40-.60) Low (.20) • Pearson product moment coefficient ® • Correlation Matrix Correlation Matrix Intercorrelations Among Teacher Practices 1 1 Choice 2 3 4 1.0 2 Directives 0.01 1.0 3 Coach 0.34 1.0 0.55 0.28 0.06 4 Positive -0.34 1.0 Descriptive Statistics • Measures of relationship – Multiple regression • Shows the relationship of several independent variables with a dependent variable • Path Analysis Application Activity? • Your students earned the following scores on your recent test: • 89, 95, 78, 50, 80, 89, 76 • What scale of measurement are you using? • What was the range? • Compute the mean, median and mode. • What is your distribution like? • The Null Hypothesis • Level of Significance – Type I Error – Type II Error • Effect Size Let’s apply this! Application Activity • If the null hypothesis is rejected, we can say that the observed results proves that the theory we are testing is true. • The null hypothesis will be rejected if the sample data turn out to be _____________ consistent/inconsistent with what one would expect if it were true. • Which level of significance offers the greater protection against Type I errors, .05 or .01? • Is it possible for a researcher to make both a Type I error and a Type II error at the same time? Application Activity • A researcher tells the superintendent at the local school that the new curriculum is statistically significantly superior to the old curriculum. What question(s) should the superintendent ask the researcher? • T-Test: • Used to compare 2 means • Analysis of Variance (ANOVA) – One Way – Two Way – Repeated Measures • Post Hoc and Planned Comparisons – E.g., Bonferoni, Tukey, Duncan’s, etc. One-Way ANOVA Stimulation Low High AD/HD Two-Way ANOVA AD/HD Treatment 1 Treatment 2 Control Treatment 1 Treatment 2 Interaction ADHD Control Behavior Treatment 1 Treatment 2 • Mixed Design Group AD/HD Control Repeated Factor Schedule Puzzle 1 Puzzle 2 Puzzle 3 • Multivariate Analysis of Variance • Analysis of Covariance (ANCOVA Nonparametric Tests • Frequencies, percentages, or proportions • Chi-square test (X2) Importance of jobs by ethnicity Race Minorities Caucasian Ignored jobs 59.1 73.1 Mentioned jobs 40.9 26.9 Chi square significance = .00787