Auxiliary DCAT - Probabilities Across...
Message/Author
 Tracy posted on Thursday, September 03, 2015 - 6:42 pm
Hi
I am unsure how to interpret the within-class proportions (not the between class chi-sq tests). For example, in my reference Class 3 below, there is a .739 probability of the children being from a low decile school, versus high. But how do I tell if this difference is significant?
Thanks.

DECILE – Cat1=Low Cat2=High
Prob S.E. Odds Ratio S.E. 2.5% C.I. 97.5% C.I.
Class 1
Category 1 0.552 0.081 1.000 0.000 1.000 1.000
Category 2 0.448 0.081 2.303 1.909 0.454 11.694
Class 2
Category 1 0.794 0.095 1.000 0.000 1.000 1.000
Category 2 0.206 0.095 0.737 0.767 0.096 5.660
Class 3
Category 1 0.739 0.153 1.000 0.000 1.000 1.000
Category 2 0.261 0.153 1.000 0.000 1.000 1.000
Chi-Square P-Value Degrees of Freedom
Overall test 3.804 0.149 2
Class 1 vs. 2 3.231 0.072 1 trending
Class 1 vs. 3 1.273 0.259 1
Class 2 vs. 3 0.082 0.775 1
 Tihomir Asparouhov posted on Thursday, September 03, 2015 - 8:32 pm
The test for the significance p1-p2 is equivalent to the significance of p1-0.5, since p2=1-p1. For that you can use the T-test T=(0.739-0.5)/0.153=1.562 with a two-sided p-value of 12%.
 Tracy posted on Thursday, September 03, 2015 - 8:43 pm
Hi Tihomir
Thanks for your help, however Im still a bit confused. Sorry.
Where is this method detailed?
Also, isnt it (0.739-.5)/.261 not .153 as .153 is class3/cat1 SE. Or am I just missing it completely?
Lastly, how do you calculate the p-value of 12% and does this 12% mean p=.88?
 Tihomir Asparouhov posted on Thursday, September 03, 2015 - 10:55 pm
Oh yeah it is .153, not .261 - I just copied it wrong - the results are correct.

This is the standard T-test

https://en.wikipedia.org/wiki/T-statistic
 Tracy posted on Friday, September 04, 2015 - 12:38 am
Thanks.
 Tracy posted on Saturday, September 05, 2015 - 1:50 am
Okay, an extension to last question, what if you have a 3-level distal category, reflecting low, mid, high:

Class 3 Prob S.E.
Category 1 0.886 0.108
Category 2 0.114 0.108
Category 3 0.000 0.000

For Class 3, can I use the following within class 3 probability t-test check?
Ho: PrCat1 = PrCat2 = PrCat3 = .333, i.e. probability of distal occurrence equal across categories.
H1: PrCat1 > .333, (with PrCat2/PrCat3 < .333).
Am interested if low distal has higher probability of occurring in class 3 (which also reflects a low plateau group on DV test).

t-statistic = (observed - expected)/SE = (.886 - .333)/.108 = 5.12, signif. at p < .001 (one tailed test). Accept H1.

Is this correct, and is this a valid use of the probability/SE in a t-test?
 Tracy posted on Monday, September 07, 2015 - 6:25 pm