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.