Table of Contents

• 1: Do those shoes fit?
• 2: Dilbert's 3 day work week
• 3: The day is saved ... or not
• 4: What you observe vs expect
• 5: The Chi-squared Equation
• 6: Give it a try
• Detour
• 7: What's a p-value?
• 8: What's a Lookup Table?
• 9: What's a "df"?
• Completing the Chi-squared Test
• 10: Interpreting a chi-squared
• 11: The answer, finally
• 12: Summary
• 13: What about 90% M/F sick days?
• 14: What about 50% M/F sick days?
• Chi-squared in Biology
• 15: Testing for a dihybrid ratio
• 16: Review and Words of Wisdom

Using the chi-squared to illuminate the grey areas:

In the last two examples (42% and 90%), it was pretty obvious what the chi-squared test would say. In this last case, where 50% of sick days fall on Monday or Friday, it's not so obvious. This is a case where the statistical test can help resolve a grey area. Here goes...

	observed ("o")	expected ("e")	(o-e)	(o-e)2	(o-e)2/e
Monday or Friday
Midweek
Total	100	100
Check

 

degrees of freedom	Χ2 crit for α = 0.05
1	3.84
2	5.99
3	7.81
4	9.49
5	11.07
6	12.59
7	14.07
8	15.51
9	16.92
10	18.31

You should have calculated  a chi-squared statistic of 4.167, and compared it to the chi-squared critical value of 3.84. So, it’s a close call, but the test says that Dilbert's random sick day model probably does NOT hold up.

The test can't tell you this for sure, but it still gives you an objective way to say "(probably) yes" or "(probably) no" when you're in a "grey" area.