Hi all, I asked this yesterday, but hadn't got any response yet. Understand
this is not pure R technical question, but more of statistical. With many
statistical experts in the list, I would appreciate any suggestions...
Many thanks
John
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Hi, I have a seemingly simple proportional test.? here is the question I am
trying to answer:
?
There is a test running each day in the lab, the test comes out as either
positive or negative. So at the end of each month, we can calculate a positive
rate in that month as the proportion of positive test results. The data look
like:
?
Month????? # positive?????? # total tests??? positive rate
January???????? 24??????????????? 205???????????? 11.7%
February??????? 31??????????????? 234???????????? 13.2%
March?????????? 26??????????????? 227???????????? 11.5%
:
:
:
August????????? 42??????????????? 241????????? 17.4%
?
The total # of positive before August is 182, and the total # of tests before
August is 1526. It appears that from January to July, the positive monthly rate
is between 11% to 13%, the rate in August is up around 17%. So the question is
whether is up in August is statistically significant?
?
I can think of 3 ways to do this test:
?
1. Use binom.test(), set ?p? as the average positive
rate between January and July (=182/1526):
?> binom.test(42,241,182/1526)
?
??????? Exact binomial test
?
data:? 42 and 241
number of successes = 42, number
of trials = 241, p-value = 0.0125
alternative hypothesis: true
probability of success is not equal to 0.1192661
95 percent confidence interval:
?0.1285821 0.2281769
sample estimates:
probability of success
???????????? 0.1742739
?
2. Use prop.test(), where I compare the average
positive rate between January & July with the positive rate in August:
?> prop.test(c(182,42),c(1526,241))
?
??????? 2-sample test for equality of
proportions with continuity correction
?
data:? c(182, 42) out of c(1526, 241)
X-squared = 5.203, df = 1,
p-value = 0.02255
alternative hypothesis:
two.sided
95 percent confidence interval:
?-0.107988625 -0.002026982
sample estimates:
?? prop 1??? prop 2
0.1192661 0.1742739
3. Use prop.test(), where I compare the average
MONTHLY positive rate between January & July with the positive rate in
August. The average monthly # of positives is 182/7=26, the average monthly $
of total tests is 1526/7=218:
?> prop.test(c(26,42),c(218,241))
?
??????? 2-sample test for equality of
proportions with continuity correction
?
data:? c(26, 42) out of c(218, 241)
X-squared = 2.3258, df = 1,
p-value = 0.1272
alternative hypothesis:
two.sided
95 percent confidence interval:
?-0.12375569? 0.01374008
sample estimates:
?? prop 1??? prop 2
0.1192661 0.1742739
?
As you can see that the method 3 gave insignificant p value compared to method 1
& 2. While I understand each method is testing different hypothesis, but for
the question I am trying to answer (does August have higher positive rate
compare to earlier months?), which method is more relevant? Or I should consider
some regression techniques, then what type of regression is appropriate?
?
Thanks for any suggestions,
?
John