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Detailed Review Concepts for Final Exam CHAPTER 1 population sample statistics parameters random samples stratified random samples incidental samples randomization nominal scales ordinal scales interval scales ratio scales discrete numbers real numbers exact scores reported scores independent variable dependent variable behavioral variables stimulus variables order of operations CHAPTER 2 frequency distribution percentiles quartiles deciles percentile ranks score interval cumulative frequency histogram frequency polygon positively skewed distribution negatively skewed distribution P50 Q2 real lower limit CHAPTER 3 mode bimodal distribution median mean nY n • (Yi - Y) = 0 i=1 n • (Yi - Y)2 i=1 mean of combined groups CHAPTER 4 yi variance s2 Yij - Yj Yj - Yt Yij - Yt within groups variance between groups variance total variance CHAPTER 5 standard deviation unbiased estimate s y2 descriptive statistics inferential statistics normal distribution Y 2s z score T score degrees of freedom CHAPTER 6 unit normal curve table of z scores and areas probabilities of z proportions under the unit normal curve percent of cases above or below z CHAPTER 7 sampling distribution Central Limit Theorem standard error confidence interval sY 1.96z alpha Y 1.96 s N Y 2.58 s N effect of N on sY CHAPTER 8 null hypothesis scientific or alternative hypothesis "significant" "not significant" p < .05 critical region Type I error Type II error power beta statistical conclusion CHAPTER 9 rxy cross-product sum of cross-products covariance scatterplot negative correlation zero correlation restriction in range causality standard error of rxy Z r sampling distribution of r Fisher's Zr Zr ± 1.96z confidence interval CHAPTER 10 Y = a + bX Y intercept (a) Slope (b) coordinate value regression line s r xy y sx standard error of estimate Y obtained Y predicted a + bX + e sy 1 - r xy2 Y 2.58sest bivariate normal distribution CHAPTER 11 xy 0 table of significance r values zr - za 1/ n-3 sy2 variance error of estimate sest2 s 2 1 - est sy2 rxy2 practical importance of rxy (Yi - Y)2 df for rxy CHAPTER 12 standard error of a statistic sampling distribution of mean differences standard error of a mean difference Y1 - Y2 sY1 - Y2 z test statistic two-tailed test practical importance of a mean difference statistical significance of a mean difference statistical assumptions for z CHAPTER 13 t at df degrees of freedom critical values of t z versus t Y sY 2 + sY 2 1 2 assumptions for the t test test statistics for N 30 and N < 30 omega squared CHAPTER 14 D sD / n z test when rxy is known correlated data two-tailed test one-tailed test percentile equivalents for levels of alpha df for correlated t test negative t CHAPTER 15 homogeneity of variance assumption single factor ANOVA t2 F Post hoc tests Type I error with multiple t tests F ratio sb2 sw2 between groups variance within groups variance b2 w2 t2 source table sum of squares SSbetween yw2 (Yt)2 /N mean square F test statistic table of F values df between df within df total sampling distribution for F F versus t omega squared assumptions for F test CHAPTER 16 correlated ANOVA model uncorrelated ANOVA model ANOVA source table for correlated data sum of squares between subjects yr2 df between df residual df total between rows variation residual df error for correlated and uncorrelated ANOVA CHAPATER 17 parametric tests nonparametric tests Type II error with nonparametric tests distribution free tests observed frequencies expected frequencies distribution when df = 30 sampling distribution of Yates' correction contingency table null hypothesis for no-association hypothesis hypothesis for z test of independent proportions df for in a contingency table df for single classification phi coefficient N = 2 N