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alternative hypothesis analysis of variance Appendix AREA FROM AREA associated assumptions attractiveness batting averages between-groups calculate chance Chapter chi-square coefﬁcient column consider correlation coefficient criterion critical value deﬁned degrees of freedom determine dichotomous distribution of scores divided drug equal estimate evaluate example expected frequencies experiment experimental F-value Factor female judges ﬁnd ﬁrst formula frequency distribution grand mean graph group means independent variable mean square measure median multiply nonparametric normal distribution null hypothesis number of groups obtained one-way analysis outcomes percentile rank population mean predicted probability problems ratio reject the null relationship reliability results of Step sample means sampling distribution sampling error San Diego Chargers scale signiﬁcance level speciﬁc standard deviation standard error statistical tests statistically signiﬁcant subtracting sum of squares t-distribution t-test teams test score tion total number type I error validity variation within-groups Z-score