00:01
So in this question we're looking at whether different types of treatment are going to affect the rate of remission in cancer cases.
00:16
So first of all what we have is that we have n equals 1500, well we have 1500 people in the study, so 1500 women in the study, and we have the number receiving a is 750 and the number receiving b is also 750.
00:42
First of all we're looking at hypotheses.
00:45
So our null hypothesis is going to be that the different treatments are independent, well let's say the probability of remission is independent of which treatment you get, the treatment a or b, and the alternate hypothesis is just going to be not that, so the probability of remission is not independent of getting treatments a or b.
01:48
So those are our hypotheses.
01:49
Now let's draw a table.
01:51
We have that we can put treatment on one axis and that can be a or b, and then we can put outcome on the other axis, and we can have remission and not remission.
02:18
So for those who got a, 160 were in remission, which means that 750 minus 160, which is 590, were not in remission.
02:31
For b, 120 were in remission, which means 750 minus 120, which is 630, were not in remission.
02:43
Now let's have a look at totals.
02:46
The total who were in remission is 280.
02:51
The total who are not in remission is 590 plus 630 is 1220.
02:59
And then the total we've got a is 750, and 750 for b, which gives 1500 total.
03:11
So now we need to make a test for an association, and our test is going to be chi -squared.
03:19
So what we're going to do is we're going to calculate chi -squared is the sum of expected minus observed squared divided by expected.
03:27
What are our expected values? well, our expected is given by the total for a row times the total for a column divided by the grand total.
03:44
So let's use that formula to populate this table with expected values in brackets.
03:52
So 280 times 750 gives me, and then divided by 1500 gives me 140.
04:01
280 times 750 divided by 1500, also 140.
04:05
And then in here we have 1220 times 750 divided by 1500, which gives 610.
04:12
And that's the same for both.
04:15
So let's calculate our chi -squared.
04:18
Our chi -squared is equal to 20 squared over 140 plus 20 squared over 140 plus, and the differences are 20 in each category, so 20 squared over 610 plus 20 squared over 610.
04:42
And this gives us a chi -squared value of 7 .026.
04:48
So that's our test statistic.
04:51
Now our number of degrees of freedom is the number of rows minus one times the number of columns minus one.
04:58
Well, in each case there's two rows and two columns, which means it's one times one, which is one degree of freedom.
05:09
So now let's find out what happened at the 0 .05 level.
05:17
Well, the p -value is the probability that chi -squared with one degree of freedom is greater than 7 .026.
05:27
And we can look this up in a table or using technology.
05:32
So i'm just going to use my computer to work this out.
05:41
And this gives me a p -value of 0 .0080, which is less than our significance level of 0 .05.
05:51
And therefore we can reject the null hypothesis, and therefore we can say there is an association between treatment type and remission rate.
06:21
Now, part c, we're also looking at stage 2 cancer...