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RESULTS & DATA ANALYSIS Descriptive Statistics Descriptive (describe) Frequencies Percents Measures mean median mode of Central Tendency Measures of Spread Range Nominal data = number of responses in each category (A’s = 4, B’s = 7, C’s = 21, D’s = 1, F’s=2) Other data = difference between responses for the greatest and least numeric values (Age of oldest is 104 and youngest is 18. Range =86 years) Tertiles, Quartiles, Quintiles Interquartile Range (IQR) Range for the 25th to 75th percentiles which captures the middle 50% Measures of Spread Standard Deviation – describes, on average, how much individual values differ from the mean Standard Scores or Z-scores – describes how many SD’s away from the sample mean an individual score or response is Normal Distribution 68% of individuals 95% of individuals >99% of individuals Sample Mean -3 SD -2 SD -1 SD +1 SD +2 SD +3 SD Inferential Statistics (Comparative) Based on Probability Tests of significance: are observed differences real differences or simply the result of chance t-test: test difference between means of two groups (t statistic) ANOVA (Analysis of Variance): test difference among three of more independent groups (F statistic) Interpreting p-values or probability value Used to decide whether the results observed are likely to reflect real differences between groups The standard is to use α = 0.05 or 5% (1 in20) t = 1.11, p =0.042 t = 1.02, p = 0.051 Probability that results observed have occurred by chance alone α = probability of Type I error (finding statistical significance when in reality there is none) Significance Statistical Practical Clinical Parametric and Non-Parametric Parametric = DV is some measured quantity (ratio or interval) so it makes sense to calculate means and SD You can draw bell curves through the data defined by two parameters…the mean and SD….hence parametric (beside, near) Non-Parametric = DV is count or rankings so means and SD have no meaning (e.g. The average religion of Americans is 2.67) Parametric Tests T-tests ANOVA (analysis of variance) Linear Regression or Multiple Linear Regression ANCOVA (analysis of covariance) – combines regression and analysis of variance Non-Parametric Tests Chi-square Logistic Regression Log-linear analysis