When is direction implied for a Chi Square test?

Hi all,
In a Chi Square goodness of fit test, and also in a Chi Square test of independence, what are the criteria for when direction can/must be stated in the conclusion?

For example, "A boy is interested in whether cricket captains call heads and tails equally at the pre-game toss. A survey of 100 matches shows that heads was called 62 times and tails 38 times. What would you conclude of the captains' calling habits?"

Running a chi square goodness of fit test I have Chi-square(1, n=100) =5.76. At p=.05, critical chi-square= 3.84, so I reject the null hypothesis. My conclusion is that "there appears to be a statistically significant difference between the captains calling heads or tails..."

Can I state in the conclusion that more heads than tails are called? Or is that beyond the power of the goodness of fit test?



Well-Known Member

You describe a very specific case of the goodness of fit test when there are only 2 groups.
you can exchange the test (one tail goodness of fit) with proportion test (with 2 tails) based on Z, and I expect you to get the same results...

Now ask yourself the same question over z test, and the answer will be easy.
Now you can change from 2 tails to one tail ...