A study was conducted to examine four methods for tutoring i

A study was conducted to examine four methods for tutoring in mathematics. Four students were randomly assigned to each method and a pretest score (x1) was obtained before tutoring began. The response of interest is a posttest score (y) and dummy variables x2, x3 and x4 were created for methods 1, 2 and 3 respectively. Variables x5, x6 and x7 are crossproduct variables for methods 1, 2 and 3 respectively, multiplied by x1. The results from fitting three regression models to these data are below. Since the posttest score is harder than the pretest, it is not unusual for x1 values to be higher than the y values.

a) Assuming that the parallelism assumption is valid, test for equality of the adjusted group means, using = .05 Write the null and alternative hypothesis, calculate an F statistic value, compare it to a tabled value and state your conclusion from the hypothesis test

b) Use the fact that the sample mean of x1 is 4.44 and the information from the model assuming parallelism but unequal intercepts, to estimate adjusted mean for each of the four groups

c) The three models for the thread data are labeled on the printout as Models 1, 2 and 3. Usually our comparisons have been between Models 1 and 2 and between Models 2 and 3. What set of parameters are being tested if we compare Model 1 to Model 3? Why is this test not usually performed, even though it is also testing for differences between groups?

                                       Tutoring data analysis results

MODEL 1

Dependent variable: y

                                    Analysis of Variance

Source   DF    Sum of Squares   Mean Square    F Value    Pr > F

Model     1         36.42785             36.42785           32.75    < .0001

Error       14       15.57215               1.11230

Total       15       52.00000

                                                        Parameter Estimates

Variable     DF    Parameter Estimate     Standard Error     t Value      Pr > | t |

Intercept     1         0.09687                        0.65050                0.15             0.8837

       x1          1      0.76690                       0.13401                5.72            < .0001

MODEL 2

Dependent variable: y

                                    Analysis of Variance

Source   DF    Sum of Squares   Mean Square    F Value    Pr > F

Model     4         44.33520             11.08380           15.91     < .0002

Error       11        7.66480               0.69680

Total       15       52.00000

                                                        Parameter Estimates

Variable       DF     Parameter Estimate     Standard Error     t Value      Pr > | t |

Intercept      1          0.75978                        0.83007                0.92             0.3797

          x1        1          0.73743                       0.12478                5.91            0 .0001

          x2        1          -1.44693                      0.59763                -2.42           0.0339

          x3       1           0.29050                       0.62935                 0.46           0.6534

          x4        1          -0.97207                        0.68276                -1.42           0.1823

MODEL 3

Dependent variable : y

                                    Analysis of Variance

Source   DF    Sum of Squares   Mean Square    F Value    Pr > F

Model     7         48.08788             6.86970           14.05       0.0006

Error       8           3.91212               0.48902

Total       15       52.00000

                                                        Parameter Estimates

Variable       DF     Parameter Estimate     Standard Error     t Value      Pr > | t |

Intercept      1          0.81818                        2.44981                0.33             0.7470

         x1         1          0.72727                       0.42169                1.72            0.1229

         x2         1           -0.65152                     2.55564                -0.25            0.8052

         x3        1           -2.81818                      2.84251                -0.99            0.3505

         x4         1           -1.81818                      2.58340                -0.70            0.5015

         x5         1           -0.16061                      0.44060                -0.36            0.7249

         x6         1            0.77273                      0.54779                  1.41            0.1960

         x7         1            0.27273                     0.48883                  0.56            0.5922

Solution