Chapter 13, Problem 26P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

Research indicates that paying students to improve their grades simply does not work (Fryer, 2011). However, paying students for specific tasks such as reading books, attending class, or doing homework does have a significant effect. Apparently, students on their own do not understand how to get good grades. If they are told exactly what to do, however, the incentives work. The following data represent a two-factor study attempting to replicate this result.

Paid for Homework | Not Paid for Homework | |

Paid for Grades | 14 | 2 |

7 | 7 | |

10 | 5 | |

9 | 7 | |

11 | 3 | |

9 | 6 | |

Not Paid for Grades | 13 | 7 |

7 | 2 | |

9 | 4 | |

7 | 2 | |

11 | 6 | |

7 | 3 |

**a.**Use a two-factor ANOVA with*α*= .05 to evaluate the significance of the main effects and the interaction.**b.**Calculate the η^{2}values to measure the effect size for the two main effects and the interaction.**c.**Describe the pattern of results. (How does paying for grades influence performance? How does paying for homework influence performance? Does the effect of paying for homework depend on whether you also pay for grades?)

**a.**

To determine

**To Find:** Using 2 factor ANOVA with

Explanation

**Given info:**

The data given as:

Category | Paid for Homework | Not paid for homework |

Paid for Grades | 14 | 2 |

7 | 7 | |

10 | 5 | |

9 | 7 | |

11 | 3 | |

9 | 6 | |

Not paid for Grades | 13 | 7 |

7 | 2 | |

9 | 4 | |

7 | 2 | |

11 | 6 | |

7 | 3 |

**Calculation:**

With the given data can easily calculate T, M and SS for all of the treatments. For paid for homework and paid for grades values are:

For paid for homework and not paid for grades values are:

For not paid for homework and paid for grades values are:

For not paid for homework and not paid for grades values are:

Also,

For a two factor study, there are 3 separate hypotheses, the two main effects and the interaction.

For Factor A, the null hypothesis states that there is no difference.

For factor B, the null hypothesis states that there is no difference in performance among the 2 treatment conditions.

For

Here, use

Sum of square total is calculated as:

Sum of square within treatment is calculated as:

Now sum of square between treatments is calculated as:

The corresponding degree of freedom is:

Now the degree of freedom within treatment is calculated as:

Similarly, the degree of freedom between treatments is calculated as:

The *MS* within treatment is calculated as:

**b.**

To determine

**To Calculate:** The

**c.**

To determine

**To Describe:** The pattern of results.

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Sect-13.3 P-3LCACh-13 P-1PCh-13 P-2PCh-13 P-3PCh-13 P-4PCh-13 P-5PCh-13 P-6PCh-13 P-8PCh-13 P-9PCh-13 P-10PCh-13 P-11PCh-13 P-12PCh-13 P-13PCh-13 P-14PCh-13 P-15PCh-13 P-16PCh-13 P-17PCh-13 P-18PCh-13 P-19PCh-13 P-20PCh-13 P-21PCh-13 P-22PCh-13 P-23PCh-13 P-24PCh-13 P-25PCh-13 P-26PCh-13 P-1RECh-13 P-2RECh-13 P-3RECh-13 P-4RE

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