Health Habits: Chi-squared Test of Independence

Contingency Tables

The table below summarizes the observed numbers of participants in the 3x3 contincency table.

Contingency Tables
				Physical Activity
Fruit Consumption				Low		Moderate		Vigorous		Total
Low		Count		69.000		206.000		294.000		569.000
		Expected count		51.902		212.894		304.204		569.000
		% within column		63.889 %		46.501 %		46.445 %		48.057 %
Medium		Count		25.000		126.000		170.000		321.000
		Expected count		29.280		120.104		171.616		321.000
		% within column		23.148 %		28.442 %		26.856 %		27.111 %
High		Count		14.000		111.000		169.000		294.000
		Expected count		26.818		110.002		157.181		294.000
		% within column		12.963 %		25.056 %		26.698 %		24.831 %
Total		Count		108.000		443.000		633.000		1184.000
		Expected count		108.000		443.000		633.000		1184.000
		% within column		100.000 %		100.000 %		100.000 %		100.000 %

Chi-Squared Tests
		Value		df		p		VS-MPR*
Χ²		14.152		4		0.007		10.809
N		1184

* Vovk-Sellke Maximum p -Ratio: Based the p -value, the maximum possible odds in favor of H₁ over H₀ equals 1/(-e p log(p )) for p ≤ .37 (Sellke, Bayarri, & Berger, 2001).

Ordinal Gamma
				95% Confidence Intervals
Gamma		Standard Error		Lower		Upper
0.103		0.044		0.016		0.189

Kendall's Tau
Kendall's Tau-b		Z		p		VS-MPR*
0.061		2.296		0.022		4.427

The ordinal gamma and Kendall's tau coefficients suggest a positive relationship between the variables, although the dependence is weak.