STAT250: Introduction to Biostatistics LAB

Chi-Square Tests

Dr. Kari Lock Morgan

In British Columbia, Canada, the cutoff data for entering school in any year is December 31st, so those born late in the year are younger than their classmates born early in the year. Are children born late in the year (and so younger than their peers) more likely to be diagnosed with Attention-Deficit Hyperactivity Disorder (ADHD)? We’ll look at data from a study[1] which involved 937,943 (huge sample!!!) children 6 – 12 years old. The data for boys is summarized below:

Birth Month \ ADHD / Diagnosed with ADHD / Not diagnosed with ADHD / Total
January – March / 6880 / 110,354 / 117,234
April – June / 7982 / 122,067 / 130,049
July – September / 9161 / 114,638 / 123,799
October - December / 8945 / 107,214 / 116,159
Total / 32,968 / 454,273 / 487,241

1)Chi-Square Test for Association

  1. State the null and alternative hypotheses.
  1. Calculate expected counts:

Birth Month \ ADHD / Diagnosed with ADHD / Not diagnosed with ADHD / Total
January – March / 117,234
April – June / 130,049
July – September / 123,799
October - December / 116,159
Total / 32,968 / 454,273 / 487,241
  1. Compare the observed counts to the expected counts. For which cells are the observed much higher than the expected? What does this mean?
  1. Calculate the chi-square statistic.
  1. Follow the instructions in the Minitab Users Guide (under Documents or our course website) to conduct the Chi-Square test. Check your work for the expected counts and the chi-square statistic, and find the p-value. (Note: sample sizes are DEFINITELY large enough here to use the theoretical chi-square distribution!)
  1. Make a conclusion in context.
  1. The corresponding data for girls is given below. Conduct the test for girls. (You can do it all in Minitab – no need to do things by hand again). Make a conclusion in context.

Birth Month \ ADHD / Diagnosed with ADHD / Not diagnosed with ADHD / Total
January – March / 1960 / 108,937 / 110,897
April – June / 2358 / 115,600 / 117,958
July – September / 2859 / 114,699 / 117,558
October - December / 2904 / 107,385 / 110,289
Total / 10,081 / 446,621 / 456,702
  1. Stop and think about the implications of this. What do you think is going on? Are you concerned?!?

2)Chi-Square Goodness of Fit Test

Combine the total birth data from boys and girls (ignoring ADHD or not) and test to see whether this data provides evidence that births are not equally distributed throughout the year.

  1. State the null and alternative hypotheses.
  1. Create the relevant table of observed counts.
  1. Calculate expected counts.
  1. Calculate the chi-square statistic.
  1. Conduct the goodness-of-fit test on Minitab to check your work and calculate the p-value.
  1. Make a conclusion in context.
  1. Ignore the variables birth month and ADHD, and perform a test to see whether male and female births are equally likely in British Columbia.

[1]Morrow, R., et. al., “Influence of relative age on diagnosis and treatment of attention-deficit/hyperactivity disorder in children,” Canadian Medical Association Journal, April 17, 2012; 184(7): 755-762.