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How to Read Tables and Interpret Statistical Tests - Crosstabs of Proportions

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Most tables created in Displayr have the same basic structure: they show percentages and contain one variable set in the rows and one or more variable sets in the columns. When both of these variable sets are non-numeric, the proportion of cases for each intersecting row/column is shown as %s in the table. You can choose whether the % is based on the Sample Size in the column, row, or total. Unless modified by a Rule, crosstabs will always use Column % for statistical testing. 
By default, arrows and font colors indicate statistical significance. These tests compare each cell's Column % to the average of the other columns in the row (for simple crosstabs without banners), see Exception (Complement) testing, and below for an example. A blue color/up arrow indicates that the numbers are significantly 'high' and a red color/down arrow indicates that they are significantly 'low'. The length of the arrow indicates the degree of statistical significance as set in the Advanced Statistical Testing Assumptions. To see the details of the test and a short description of what is being compared, right-click the cell and select Statistical Test. Read on to better understand how the comparisons work.

A gentle introduction to interpreting the default significance tests

The table below shows a crosstab showing unaided awareness by Age, Gender, and Current Provider. The table shows Column %, and all the significance tests are conducted using this statistic (i.e., even if you change the statistic, the test will still be a test of Column %). The interpretation of the tests on this table is as follows:

  • Age is a determinant of aided awareness. In particular, younger people are more likely to be aware of Vodafone and Virgin Mobile.
  • Gender is not a determinant of unaided awareness.
  • Current provider is a determinant of unaided awareness.

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A more technical explanation

The next table is identical to the first in how its significance tests are interpreted. In this case, it is showing a crosstab of a Pick One question, Preferred Cola, by a Pick Any question, Age within Gender.

The table below shows a table exported to Office.

 

CrosstabProportion2.png

Preferred cola by Age within genderTotal sample; Unweighted; base n = 322; total n = 327; 5 missing; Multiple comparison correction: None (p = 0.05); Minimal sample size for testing: 2

The top-left corner of this table shows that amongst people in the sample who are both Male and aged 18 to 24, 71% prefer Coca-Cola. The arrow to the right of the 71% indicates that males aged 18 to 24 are more likely to prefer Coca-Cola than the adult population as a whole (i.e., this is the interpretation of a significance test). More specifically:

  • The 71% observed amongst the males aged 18 to 24 is significantly different from the percentage preferring Coca-Cola amongst the rest of the sample (i.e., the percentage amongst the combined group of all the women, and all the men aged 25 or more). The percentage amongst the rest of the sample is not shown in the table, but can be computed from it as 42% (i.e., (49%×49 + 38%×87 + 59%×22 + 51%×59 + 33%×84)/(322 - 21)). Thus, the significance test compared 71% with 42%. Or, stated in slightly different language: each column is compared with its complement.
  • The 71% observed amongst the 18 to 24 males is higher than the percentage observed amongst the rest of the sample (this is communicated by the direction of the arrow).
  • The result is significant at approximately the 0.01 level (this is communicated by the arrow’s length). The 0.01 level of significance is equivalent to the 99% confidence level.

The table footer contains additional information about how the testing was conducted. It shows that: arrows have only been presented where tests have been significant at the 0.05 level; no tests were conducted involving groups with sample sizes of less than 2; and no multiple comparison correction was applied.

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How to Apply Significance Testing in Displayr

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