7/27 - chi-square-test

A simple way of testing whether there is any significant association between household type in 1991 and living in a communal establishment in 2001 is a chi square test. This test is performed on a crosstabulation of two variables. In order to focus on our question, we need to simplify our table so that in 2001 we only measure residence in a private household versus residence in a communal establishment (otherwise other types of transition would affect the test).

Living arrangement in 2001 by household type by 1991, residents in private households aged 65 or over in 1991 (%)
      Household type 1991
      
Living arrangement 2001
 One person
 Couple only
Couple plus other(s)
Lone parent plus other(s) inc. offspring
Other
Total
Private household
 86.8 95.1 97.6
 92.6
 87.9
 92.2
 Communal establishment
 13.2
  4.9 2.4
 7.4
 12.1
 7.8
 Total  100  100 100
 100
 100
 100
Pearson chi2 (4 d.f.) = 824.8149, pr = 0.0000

The chi square value is very high at 824.8 and statistically significant well below the 0.001 level. There is good reason to believe that entering a communal establishment is associated with type of household.

Command to create chi square statistic
  Where livarr01 is residence in private household or CE in 2001 and hhtype91 is household type in 1991.
 STATA tab livarr01 hhtype91, col nofreq chi2
 SPSS crosstabs /tables livarr01 by hhtype91 /cells=col /stat=chisq.
 SAS proc freq data=dataname; (where dataname is the name of the dataset)
table livarr01*hhtype91 /chisq;

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