## MS Mod 14 Two-factor ANOVA interaction practice exam questions

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K MS Module 14 Two-factor ANOVA interaction practice exam questions(The attached PDF file has better formatting.) A two-factor classification table has two rows, two columns, and two observations in each cell.    Column 1    Column 2Row 1    32; 33    32; 27Row 2    14; 29    20; 22We use analysis of variance to test ●    whether the Row 1 mean differs from the Row 2 mean    ○    the null hypothesis is that the row means are equal●    whether the Column 1 mean differs from the Column 2 mean    ○    the null hypothesis is that the column means are equal●    whether the interaction effects are significant    ○    the null hypothesis is that the interaction effects are zeroQuestion 14.1: Square of sum of observationsWhat is the square of the sum of all the observations, or x...2 ?Answer 14.1: (32 + 33 + 32 + 27 + 14 + 29 + 20 + 22)2 = 43,681Question 14.2: Correction factorWhat is the correction factor used for the total sum of squares and the treatment sums of squares (for both rows and columns)?Answer 14.2: 43,681 / 8 = 5,460.125(correction factor = the square of the sum of the observations / the number of observations)Question 14.3: Sum of squares of observationsWhat is the sum of the squares of all the observations, or i j k xijk2 ?Answer 14.3: (322 + 332 + 322 + 272 + 142 + 292 + 202 + 222) = 5,787Question 14.4: Sum of squares of totals by cellWhat is the sum of the squares of the totals in each cell, or i j xij2 ?Answer 14.4: (32 + 33)2 + (32 + 27)2 + (14 + 29)2 + (20 + 22)2 = 11,319Question 14.5: Sum of squares of row totalsWhat is the sum of the squares of the row totals, or j xi..2Answer 14.5: (32 + 33 + 32 + 27)2 + (14 + 29 + 20 + 22)2 = 22,601Question 14.6: Sum of squares of column totalsWhat is the sum of the squares of the column totals, or j x.j.2Answer 14.6: (32 + 33 + 14 + 29)2 + (32 + 27 + 20 + 22)2 = 21,865Question 14.7: Total sum of squaresWhat is SST, the total sum of squared deviations?Answer 14.7: 5,787 – 5,460.125 = 326.875(total sum of squares = the sum of the squares of all the observations – the correction factor)Question 14.8: SSAWhat is SSA, the sum of squared deviations for the i dimension (the rows)?Answer 14.8: 22,601 / 4 – 5,460.125 = 190.125(SSA = the sum of the squares of the row totals / observations per row – the correction factor)Question 14.9: SSBWhat is SSB, the sum of squared deviations for the j dimension (the columns)?Answer 14.9: 21,865 / 4 – 5,460.125 = 6.125(SSB = the sum of the squares of the column totals / observations per column – the correction factor)Question 14.10: Error sum of squaresWhat is SSE, the error sum of squared deviations?Answer 14.10: 5,787 – 11,319 / 2 = 127.50(error sum of squares = the sum of the squares of the observations – the sum of the squares of the totals in each cell / number of observations by cell)Question 14.11: SSABWhat is SSAB, the sum of squared deviations for the interaction?Answer 14.11: 326.875 – 190.125 – 6.125 – 127.50 = 3.125Question 14.12: Degrees of freedomWhat are the degrees of freedom for the rows (SSA)?Answer 14.12: 2 – 1 = 1(the degrees of freedom for the rows = number of rows – 1)Question 14.13: Degrees of freedomWhat are the degrees of freedom for the columns (SSB)?Answer 14.13: 2 – 1 = 1(the degrees of freedom for the columns = number of columns – 1)Question 14.14: Degrees of freedomWhat are the degrees of freedom for the interaction effects (SSAB)?Answer 14.14: (2 – 1) × (2 – 1) = 1(the degrees of freedom for the interaction effects = (number of rows – 1) × (number of columns – 1)Question 14.15: Degrees of freedom What are the degrees of freedom for the total sum of squares (SST)?Answer 14.15: 8 – 1 = 7(the degrees of freedom for the total sum of squares = number of observations – 1)Question 14.16: Degrees of freedom What are the degrees of freedom for the error sum of squares (SSE)?Answer 14.16: 7 – 1 – 1 – 1 = 4(degrees of freedom for SSE = degrees of freedom for SST – degrees of freedom for SSA – degrees of freedom for SSB – degrees of freedom for SSAB)Question 14.17: Mean squared deviation for the rowsWhat is MSA, the mean squared deviation for the rows?Answer 14.17: 190.125 / 1 = 190.125(MSA = SSA / degrees of freedom)Question 14.18: Mean squared deviation for the columnsWhat is MSB, the mean squared deviation for the columns?Answer 14.18: 6.125 / 1 = 6.125(MSB = SSB / degrees of freedom)Question 14.19: Mean squared deviation for the interactionWhat is MSAB, the mean squared deviation for the interaction?Answer 14.19: 3.125 / 1 = 3.125(MSAB = SSAB / degrees of freedom)Question 14.20: Mean squared errorWhat is MSE, the mean squared error?Answer 14.20: 127.50 / 4 = 31.875(MSE = SSE / degrees of freedom)Question 14.21: F valueWhat is fA, the f value for testing significance of the row differences?Answer 14.21: 190.125 / 31.875 = 5.965(fA, the f value for testing significance of the row differences, is MSA / MSE)Question 14.22: F valueWhat is fB, the f value for testing significance of the column differences?Answer 14.22: 6.125 / 31.875 = 0.192(fB, the f value for testing significance of the column differences, is MSB / MSE)Question 14.23: F valueWhat is fAB, the f value for testing significance of the interaction effect?Answer 14.23: 3.125 / 31.875 = 0.098(fAB, the f value for testing significance of the interaction effect, is MSAB / MSE) Attachments MS Module 14 Two-factor ANOVA interaction practice exam questions.pdf (241 views, 43.00 KB)
##### Merge Selected
Merge into selected topic...

Merge into merge target...

Merge into a specific topic ID...