# Increase in the number of independent variables in...

## Increasing the number of independent variables in the construction of cross-tabulation tables

You can build cross-tabulation tables by capturing the values ​​of several independent variables.

There are four possible situations [30].

First, sometimes adding one more independent variable clarifies the mechanism of the previously discovered dependency. So, by calculating the cross-tabulation table between the marital status (independent variable) and the level of acquiring fashionable clothing (Table 12.13), one would think that many men and women after marriage or marriage lose interest in buying fashionable clothes.

Table 12.13. Distribution of persons with different marital status by the number of fashionable clothes they acquire,%

 Get fashionable clothes Marital status All respondents Married Single (not married) Many 31 52 37 Not enough 69 48 63 Total 100 (700) 100 (300) 100 (1000)

However, the inclusion in the analysis of another independent variable - the sex of the respondent (Table 12.14) shows that this pattern is manifested only in women, and it is more pronounced than in the respondents as a whole.

Table 12.14. Distribution of persons of different sexes and with different marital status by the number of fashionable clothes they acquire,%

 Acquire fashionable clothing Sex All Interviewed Men Women Marital status Marital status Married Single Married Single Many 35 40 25 60 37 Not enough 65 60 75 40 63 Total 100 (400) 100 (120) 100 (300) 100 (180) 100 (1000)

Secondly, it sometimes turns out that the previously observed dependence was illusory, the so-called false correlation ; that in fact there is another factor, the variation of which explains the observed effects. So, the tab. 12.15 gives the impression that people with higher education often purchase expensive car brands.

Table 12.15. The presence of an expensive brand car in people with different education,%

 The presence of an expensive car Education All Interviewed Higher not higher Yes 32 21 24 No 68 79 76 Total 100 (250) 100 (750) 100 (1000)

The inclusion in the analysis of another independent variable - the income of the respondent (Table 12.16) - shows that education in itself does not affect the probability of buying an expensive car; the true cause of the observed differences is the level of income that people with higher education tend to have higher.

Table 12.16. The presence of an expensive brand car in persons with different incomes and education,%

 Availability expensive car Revenue All respondents Low high Education Education Higher not higher Higher not higher Yes 20 20 40 40 No 80 80 60 60 Total 100 100 100 100 100 (100) (700) (150) (50) (1000)

Thirdly, sometimes adding one or more independent variables allows us to reveal a previously hidden dependence. For example, an attempt to identify the assumed link between age and interest in traveling abroad has failed (Table 12.17).

Table 12.17. Interest in overseas tourism in persons of different ages,%

 Interest in overseas tourism Age All Interviewed up to 45 years old 45 years and older Interested 50 50 50 Not interested 50 50 50 Total 100 (500) 100 (500) 100 (1000)

Dividing the same respondents by sex (Table 12.18), the researchers found the desired dependency, which in men and women was multidirectional.

Table 12.18. Interest in overseas tourism in persons of different sex and age,%

 Interest in overseas tourism Sex All respondents Men Women Age Age up to 45 years old 45 years and older up to 45 years old 45 years and older Interested 60 40 35 65 50 Not interested 40 60 65 35 50 Total 100 (300) 100 (300) 100 (200) 100 (200) 100 (1000)

Finally, fourthly, it is possible that the inclusion of independent variables in the analysis does not change anything in relation to the previously identified or, conversely, unidentified pairing pattern.

In general, increasing the number of independent variables when building cross-tabulation tables is useful. But you should not abuse this. It is impossible to allow the formation of so small groups in rows and columns in the analysis, so that the condition fe ≥ 5 is violated, where fe is the expected number of respondents in the cell of the cross-tabulation table, assuming that its rows and columns are independent.

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