00:01
So there's a newspaper article that describes a study whether stress management can help reduce heart attacks.
00:07
And so there was a total of 107 subjects that had reduced blood flow to the heart and were at risk of heart attack.
00:17
And so they were randomly assigned to one of three groups.
00:22
They went to either a stress management program, a four -month exercise program, and a third received just the usual heart care from their personal physicians.
00:32
And both of the, all three of these were four -month treatments.
00:36
Four -month treatments.
00:39
And then within those four months, or excuse me, over the next three years, i should say, three of the 33 people in the stress management group suffered some cardiac event, whereas seven of the 34 who were involved in the exercise group had a cardiac event.
01:01
And 12 out of the 40 people in the usual care suffered these cardents.
01:10
And we wanna know the success rates of the three treatments.
01:17
So the success rates of each treatment.
01:19
So in order to do that, what we need to do is figure out how many people were in the no cardiac event, because a successful treatment would mean that no one had a cardiac, right? i would say a successful treatment, you'd have no cardiac event.
01:33
So the probability of success will equal the number of no cardiac events, no cardiac events, over the total in that treatment, total in the treatment group.
02:10
So we need to figure that out.
02:12
So we know three had cardiac.
02:13
That means 33 did not, or excuse me, 30 did not have a cardiac event.
02:18
If seven had a cardiac event, that means 34 minus seven, which would be 27, had no cardiac event.
02:25
And then 12 minus, 12 taken away from 40 would be 28.
02:28
And so we just take the ratios of those and we end up with 0 .909 for the stress management group, 0 .794 for the exercise group, and then 0 .7 for the usual care group.
02:46
And you can round to your precision there.
02:48
If we're going to two decimals, i guess it gets for the stress group, we'd probably say 0 .91.
02:54
And then we wanna find the expected counts.
02:58
We're gonna, under the assumption that there'd be no difference among the groups.
03:04
So if there's no difference among the groups, one thing we could say is that it's independent.
03:08
So a null hypothesis of no difference, no difference between groups, that's equivalent to the cardiac events are independent of the program.
03:26
So cardiac events are independent of treatment.
03:56
Whereas the alternative would be not independent.
04:02
There is a dependent relationship between the cardiac events and treatment.
04:06
So not independent.
04:15
All right, so, and this is not, we're not really gonna do much more with the proportions here because we're gonna do this with a chi -squared statistic.
04:27
Because we're looking for, it's a chi -squared test for independence.
04:30
That's what we're gonna do.
04:31
So we need to find the expected counts.
04:33
Because the chi -squared statistic is calculated as the sum of the observed values minus the expected values squared divided by the expected values.
04:43
So we need the expected values.
04:45
And so for that, we need the totals.
04:47
So we have the total rows here, the totals across the rows.
04:50
We already have the totals in the columns.
04:52
We need the total in the rows.
04:53
And to find the expected counts, what we do is take the total in the row multiplied by the total in the column divided by the total in the study.
05:05
So for example, to find the expected count for the cardiac event in the stress program, what we do is we take the total in the row, 22, multiplied by 33, the total in the column, and then that would give us this value here.
05:20
And then we'd have to divide by 107.
05:23
And we do that for each cell.
05:25
So for example, the no cardiac event in the exercise program would be 85 times 34 divided by 107...