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CHAPTER 12 Becoming Acquainted With Statistical Concepts Why We Need Statistics • Statistics is an objective way of interpreting a collection of observations. • Types of statistics - Descriptive techniques - Correlational techniques - Differences among groups Univariate and multivariate How Computers Are Used in Statistics • Frequently used in offices, labs, and homes for statistical analysis • Types of software for statistics - Biomedical Series (BIMED) - Statistical Analysis System (SAS) - Statistical Package for the Social Sciences (SPSS) Measures of Central Tendency and Variability • Central tendency scores - Mean: Average - Median: Midpoint - Mode: Most frequent • Variability scores - Standard deviation - Range of scores Categories of Statistical Tests • Parametric - Normal distribution - Equal variances - Independent observations • Nonparametric (distribution free) - Distribution is not normal • Normal curve - Skewness - Kurtosis Normal Curve Skewness Kurtosis Statistics • What statistical techniques tell us - Reliability (significance) of effect - Strength of the relationship (meaningfulness) • Types of statistical techniques - Relationships among variables - Differences among groups Interpreting Statistical Findings • Probability - Alpha: false positive (type I error) • Typical: p < .05 or p < .01 - Beta: false negative (type II error) • Meaningfulness (effect size) • Power: Probability of rejecting the null hypothesis when it is false Truth Table for the Null Hypothesis H0 true H0 false Accept Correct decision Type II error (beta) Reject Type I error (alpha) Correct decision Alpha & Beta • Alpha = p-level in statistical tests • 1 - Beta = the power of the statistical test Ways to Statistical Power • alpha (often preset to .05 or .01) • beta (often preset to .20) • N Statistical Power and Effect Size • Effect size is invariant • Overpower = greater N than needed to statistically detect the effect (detect trivial effects) • Underpower = not enough N to statistically detect the effect (can’t detect meaningful effects) • Appropriate statistical power is achieved from an a priori power analysis Power Analysis • Effect size = statistical power • With the info of effect size, alpha, and beta, power analysis can tell us what N we need for the study • Tables, computer programs, and math equations