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My question is whether it is appropriate to use chi-square to determine statistical significance where the independent variable is the number of years of program operation in a medical practice (i.e., Years 1, 2, and 3) and the dependent variable is the number of patients from the practice who have at least one inpatient hospitalization each year. My concern is that because the practice grew each year many, but not all, of the patients in each of the three years are the same. The raw data shows a big decrease in the number of inpatient hospitalizations from the first year to the third year relative to the total number of patients. I’m looking for a way to determine whether the difference is statistically significant and I’ve put the data into chi-square format (see attached picture).

If chi-square analysis for this data is not appropriate, can you suggest something else? I do not have the individual data, just the group data as displayed in the table. Thanks for your help with this.enter image description hereenter image description here

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    $\begingroup$ What question are you trying to ask of your data? It isn't at all evident from their description. $\endgroup$
    – whuber
    Commented Mar 29, 2018 at 20:36
  • $\begingroup$ I am trying to determine whether the reduction in hospitalizations from year 1 to year 3 is statistically significant. The actual numeric reduction from Year 1 to Year 3 (from 43 to 35) is 18%, but the number of patients increased from year 1 to year 3 from 234 to 328, so the percentage of patients hospitalized in year 1 was 18.38, whereas in year 3 the percentage was 10.67, which seems impressive - but we would like to know if the change is statistically significant. Thanks. $\endgroup$ Commented Mar 30, 2018 at 14:39

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You could use chi square as you propose, or maybe a binomial glm with time as covariate.

For a similar example, see Testing for significant difference in mortality rate between multiple groups

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