**Sociology
405/805**

**Problem
Set 4**

**Due
Friday, March 3, 2000**

1. This question asks you to look for
interaction between two variables when conducting a two-way analysis of
variance. Select a ordinal or higher
level dependent variable in the *703.sav*
data set and two explanatory variables.
Using the *Statistics-General
Linear Model-Simple Factorial* procedure (with the *Unique* method), obtain a two-way analysis of variance. In order to observe and describe the
possible interaction among the two explanatory variables, first examine all the
means using *Statistics-Compare
Means-Means* with two layers for the independent list. Then use *Statistics-General
Linear Model-GLM General Factorial* to obtain the same analysis of
variance. But in this latter case,
obtain the *Plots* to produce a line
diagram that shows the possible interaction.
These lines should match up with the means from the *Means* procedure. Organize
all the results, state the conclusions of the analysis of variance, and write a
note explaining what the results show.
(If you do not find a significant interaction, that is all right, but in
this case present the results showing that there is no statistically
significant interaction). * *

2. In *The Nation* of April 27,
1992, the following table appeared.

Country |
Per Cent of Labour Force which is Managers |
Productivity Growth (per cent per year) |

United States |
12.1 |
0.7 |

Australia |
11.9 |
0.9 |

Canada |
11.9 |
1.2 |

Germany |
6.2 |
0.8 |

Austria |
4.7 |
1.9 |

Japan |
3.7 |
3.0 |

Netherlands |
3.3 |
1.5 |

Denmark |
3.0 |
2.1 |

Finland |
3.0 |
3.6 |

Greece |
1.8 |
-0.5 |

Spain |
1.3 |
3.0 |

The author of the article, Andrew L. Shapiro, noted “The United States has the most managers per employee, yet during the past decade our industrial output has grown the least of all the nineteen major industrial nations. … There seems to be an inverse relationship throughout between management size and productivity.” Draw the scatter diagram, compute the Pearson and Spearman correlation coefficients, and test each for statistical significance. Do the data support Shapiro’s argument? Write a short note on the data and Shapiro’s argument, and note any anomalies.