## MS Mod 9 and 10 Single-Factor ANOVA and Levene’s test practice exam...

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K MS Modules 9 and 10 Single-Factor ANOVA and Levene’s test practice exam questions(The attached PDF file has better formatting.)A experiment has three groups and four observations in each group.obsv →     1    2    3    4group 1    14    22    16    14group 2    12    15    14    25group 3    7    17    24    32The groups are normally distributed with the same variance. The null hypothesis is that the means of the groups are the same: H0: μ1 = μ2 = μ3 Question 10.1: Square of the sum of the observationsWhat is the square of the sum of all the observations, or x..2 ?Answer 10.1: (14 + 22 + 16 + 14 + 12 + 15 + 14 + 25 + 7 + 17 + 24 + 32)2 = 44,944Question 10.2: Sum of the squares of the observationsWhat is the sum of the squares of all the observations, or i j xij2 ?Answer 10.2: 142 + 222 + 162 + 142 + 122 + 152 + 142 + 252 + 72 + 172 + 242 + 322 = 4,260Question 10.3: Total sum of squaresWhat is SST, the total sum of squares?Answer 10.3: 4,260 – 44,944 / 12 = 514.67(the total sum of squares = the sum of the squares of all the observations – the square of the sum of all the observations / the number of observations)Question 10.4: Sums of squares of group totalsWhat is the sum of squares of the group totals?Answer 10.4: (14 + 22 + 16 + 14)2 + (12 + 15 + 14 + 25)2 + (7 + 17 + 24 + 32)2 = 15,112Question 10.5: Treatment sums of squaresWhat is SSTr, the treatment sum of squares?Answer 10.5: 15,112 / 4 – 44,944 / 12 = 32.67(treatment sums of squares = the sum of squares of the group totals / the number of observations per group – the square of the sum of all the observations / the total number of observations)Question 10.6: Error sum of squaresWhat is SSE, the error sum of squares?Answer 10.6: 514.67 – 32.67 = 482.00(error sum of squares = total sum of squares – treatment sums of squares)Question 10.7: Total degrees of freedomWhat are the total degrees of freedom?Answer 10.7: 12 – 1 = 11(total degrees of freedom = number of observations – 1)Question 10.8: Degrees of freedom for the groupsWhat are the degrees of freedom for the groups?Answer 10.8: 3 – 1 = 2(degrees of freedom for the groups = number of groups – 1)Question 10.9: Degrees of freedom for the error sum of squaresWhat are the degrees of freedom for the error sum of squares?Answer 10.9: 11 – 2 = 9(degrees of freedom for the error sum of squares = total degrees of freedom – degrees of freedom for the groups)Question 10.10: Mean squared deviation for the groupsWhat is MSTr, the mean squared deviation for the groups?Answer 10.10: 32.667 / 2 = 16.33(mean squared deviation for the groups = treatment sums of squares / degrees of freedom for the groups)Question 10.11: Mean squared errorWhat is MSE, the mean squared error?Answer 10.11: 482 / 9 = 53.556(mean squared error = error sum of squares / degrees of freedom for the error sum of squares)Question 10.12: F value What is the F value for testing the null hypothesis?Answer 10.12: 16.333 / 53.556 = 0.305( F value = treatment mean square / mean squared error)Levene’s methodLevene’s method tests whether the group variances are the same. The groups are normally distributed, and the null hypothesis is that the variances are the same: H0: σ21 = σ22 = σ23 [σ2j is the variance of Group j ].Question 10.13: Absolute deviationsWhat are the absolute deviations of the observations in each group?Answer 10.13: absolute deviation = absolute value of cell value – group meanobsv →     1    2    3    4    Meangroup 1    14.0    22.0    16.0    14.0    16.5group 2    12.0    15.0    14.0    25.0    16.5group 3    7.0    17.0    24.0    32.0    20.0absolute deviations                sample variancegroup 1    2.5    5.5    0.5    2.5    14.333group 2    4.5    1.5    2.5    8.5    33.667group 3    13.0    3.0    4.0    12.0    112.667Question 10.14: Sample varianceWhat is the sample variance in each group?Answer 10.14: the sample variances indicate whether the variances appear to differ significantly; the group means do not differ much here, but the sample variances differ greatlyQuestion 10.15: Square of sum of absolute deviationsWhat is the square of the sum of the absolute deviations?Answer 10.15: (2.5 + 5.5 + 0.5 + 2.5 + 4.5 + 1.5 + 2.5 + 8.5 + 13 + 3 + 4 + 12)2 = 3,600Question 10.16: Sum of squares of absolute deviationsWhat is the sum of the squares of the absolute deviations?Answer 10.16: (2.52 + 5.52 + 0.52 + 2.52 + 4.52 + 1.52 + 2.52 + 8.52 + 132 + 32 + 42 + 122) = 482Question 10.17: Total sum of squares (SST) for Levene’s test What is the total sum of squares (SST) for Levene’s test?Answer 10.17: 482 – 3,600 / 12 = 182(the total sum of squares = the sum of the squares of all the observations – the square of the sum of all the observations / the number of observations)Question 10.18: Sums of squares of group totalsWhat is the sum of squares of the group totals for Levene’s test?Answer 10.18: (2.5 + 5.5 + 0.5 + 2.5)2 + (4.5 + 1.5 + 2.5 + 8.5)2 + (13 + 3 + 4 + 12)2 = 1,434Question 10.19: Treatment sums of squaresWhat is SSTr, the treatment sum of squares for Levene’s test?Answer 10.19: 1,434 / 4 – 3,600 / 12 = 58.50(treatment sums of squares = the sum of squares of the group totals / the number of observations per group – the square of the sum of all the observations / the total number of observations)Question 10.20: Error sum of squaresWhat is SSE, the error sum of squares for Levene’s test?Answer 10.20: 182 – 58.50 = 123.50(error sum of squares = total sum of squares – treatment sums of squares)Question 10.21: Total degrees of freedomWhat are the total degrees of freedom for Levene’s test?Answer 10.21: 12 – 1 = 11(total degrees of freedom = number of observations – 1)Question 10.22: Degrees of freedom for the groupsWhat are the degrees of freedom for the groups for Levene’s test?Answer 10.22: 3 – 1 = 2(degrees of freedom for the groups = number of groups – 1)Question 10.23: Degrees of freedom for the error sum of squaresWhat are the degrees of freedom for the error sum of squares for Levene’s test?Answer 10.23: 11 – 2 = 9(degrees of freedom for the error sum of squares = total degrees of freedom – degrees of freedom for the groups)Question 10.24: Mean squared deviation for the groupsWhat is MSTr, the mean squared deviation for the groups for Levene’s test?Answer 10.24: 58.50 / 2 = 29.25(mean squared deviation for the groups = treatment sums of squares / degrees of freedom for the groups)Question 10.25: Mean squared errorWhat is MSE, the mean squared error for Levene’s test?Answer 10.25: 123.50 / 9 = 13.722(mean squared error = error sum of squares / degrees of freedom for the error sum of squares)Question 10.26: F value What is the F value for testing the null hypothesis for Levene’s test?Answer 10.26: 29.25 / 13.722 = 2.132( F value = treatment mean square / mean squared error) Attachments MS Module 9 Single-Factor ANOVA practice exam questions.pdf (251 views, 53.00 KB)
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