Descriptive Statistics—379

The quantiles of SLEEP2 are plotted on the vertical axis of each graph. (We moved one of the graphs to make the plots a bit easier to see.) The QQ-plot of the underlying distribution should lie on a straight line. In this example, none of the QQ-plots lie on a line, indicating that the distribution of SLEEP2 does not match any of those in the group DIST.

Descriptive Statistics

The first two views display the summary statistics of each series in the group. Details for each statistic are provided in “Descriptive Statistics” on page 310.

•Common Sample computes the statistics using observations for which there are no missing values in any of the series in the group (casewise deletion of observations).

•Individual Samples computes the statistics using all nonmissing observations for each series (listwise deletion).

The two views are identical if there are no missing values, or if every series has missing observations at the same observation numbers.

In addition, you may elect to display a statistical graph containing boxplots:

•Boxplots computes and displays boxplots for each series. See “Boxplots” on page 409 for details.

380—Chapter 12. Groups

Tests of Equality

This view tests the null hypothesis that all series in the group have the same mean, median (distribution), or variance. All of these tests are described in detail in “Equality Tests by Classification” on page 318.

The Common sample option uses only observations for which none of the series in the group has missing values.

As an illustration, we demonstrate the use of this view to test for groupwise heteroskedasticity. Suppose we use data for seven countries over the period 1950–1992 and estimate a pooled OLS model (see Chapter 27, “Pooled Time Series,

Cross-Section Data”, on page 825). To test whether the residuals from this pooled regression are groupwise heteroskedastic, we test the equality of the variances of the residuals for each country.

First, save the residuals from the pooled OLS regression and make a group of the residuals corresponding to each country. This is most easily done by estimating the pooled OLS regression using a pool object and saving the residuals by selecting Proc/Make Residuals in the pool object menu or toolbar.

Next, open a group containing the residual series. One method is to highlight each residual series with the right mouse button, double click in the highlighted area and select Open Group. Alternatively, you can type show, followed by the names of the residual series, in the command window.

Select View/Tests of Equality…, and choose the Variance option in the Test Between Series dialog box.

382—Chapter 12. Groups

Many of the settings will be familiar from our discussion of one-way tabulation in “One-Way Tabulation” on page 325.

Group into Bins If

If one or more of the series in the group is continuous and takes many distinct values, the number of cells becomes excessively large. This option provides you two ways to automatically bin the values of the series into subgroups.

•Number of values option bins the

series if the series takes more than the specified number of distinct values.

•Average count option bins the series if the average count for each distinct value of the series is less than the specified number.

•Maximum number of bins specifies the approximate maximum number of subgroups to bin the series. The number of bins may be chosen to be smaller than this number in order to make the bins approximately the same size.

The default setting is to bin a series into approximately 5 subgroups if the series takes more than 100 distinct values or if the average count is less than 2. If you do not want to bin the series, unmark both options.

NA Handling

By default, EViews drops observations from the contingency table where any of the series in the group has a missing value. Treat NA as category option includes all observations and counts NAs in the contingency table as an explicit category.

Layout

This option controls the display style of the tabulation. The Table mode displays the categories of the first two series in r × c tables for each category of the remaining series in the group.

The List mode displays the table in a more compact, hierarchical form. The Sparse Labels option omits repeated category labels to make the list less cluttered. Note that some of the conditional χ2 statistics are not displayed in list mode.

384—Chapter 12. Groups

χ2 with IJK− ( I − 1 )−( J − 1) − ( K − 1) − 1 degrees of freedom where I, J, K are the number of categories for each series.

These test statistics are reported at the top of the contingency table:

Tabulation of LWAGE and UNION and MARRIED

Date: 012/15/00 Time: 14:12

Sample: 1 1000

Included observations: 1000

Tabulation Summary

WARNING: Expected value is less than 5 in 40.00% of cells (8 of 20).

In this group, there are three series LWAGE, UNION, and MARRIED, each with

I = 5 , J = 2 , and K = 2 categories. Note the WARNING message: if there are many cells with expected value less than 5, the small sample distribution of the test statistic under the null hypothesis may deviate considerably from the asymptotic

χ2 distribution.

•Conditional independence between series in the group. If you display in table mode, EViews presents measures of association for each conditional table. These measures are analogous to the correlation coefficient; the larger the measure, the

larger the association between the row series and the column series in the table. In addition to the Pearson χ2 for the table, the following three measures of association

are reported:

where min( r, c) is the smaller of the number of row categories r or column catego-

˜

ries c of the table, and N is the number of observations in the table. Note that all three measures are bounded between 0 and 1, a higher number indicating a stronger relation between the two series in the table. While the correlation coefficient only measures the linear association between two series, these nonparametric measures are robust to departures from linearity.