We conducted a test on two groups (A and B). We used a
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could we
draw from the data?
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
We conducted a test on two groups (A and B). We used a
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could we
draw from the data?
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
We conducted a test on two groups (A and B). We used a
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could we
draw from the data?
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
Cosine 在 2021年4月29日 星期四下午3:08:08 [UTC+8] 的信中寫道：
We conducted a test on two groups (A and B). We used a
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could we
draw from the data?
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
We could intitutively connect the P-value inference with the CI
inference by P-value < alpha <=> reject H0 <=> ( 1-alpha )CI doesn't
consists of 0. But is there a formal way to prove the latter part,
i.e, making inference by CI?
We could also draw the conclusion of clinical significance if we
have additional information on a clinically meaningful value. Then we
could say that the result is clinically significant if 1) the CI
consists of that clinical measure, and 2) the width of the CI is
narrow enough. Nevertheless, are there ways to determine if the width
of the CI is too wide objectively?
On Thu, 29 Apr 2021 00:08:06 -0700 (PDT), Cosine <ase...@gmail.com>
wrote:
We conducted a test on two groups (A and B). We used a
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could weBad reporting. Is the N a total, for equal group sizes?
draw from the data?
Whatever the "cases" are, they are vastly different in SD.
Perhaps Case 1 has scores near zero for all. Or: It will be more
sensible if Case 1 happened to report "Average item score"
whereas the others reported "Scale Total". That would make
the adjusted line for Case 1 read
1 2.25 0.001 0.75-3.75 2000
I haven't done calculations to be sure, but that does
seem like a large SE (on all three) for the reported Ns and
a 15 point scale.
Then too, some numbers have to be wrong. For Case
3, the mean difference is the midpoint of (-1.1, 3.7), not
of the reported (-2.1, 3.7). I assume -1.1 is correct.
But, more seriously, the test results (CI) are inconsistent with
the reported p-values. The SE for each comparison, the
denominator of the t-tests, is about 1/4th the range of the
CI. Using that for a close approximation gives me t-tests of
3.0, 4.94, and 1.08, respectively. The difference for case 2
is clearly the largest, and it is smaller than "p-value = 0.005".
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:If this is a homework assignment, as Duncan suggests,
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
you should give credit where credit is due.
--
Rich Ulrich
Rich Ulrich ? 2021?4?30? ?????1:58:02 [UTC+8] ??????
On Thu, 29 Apr 2021 00:08:06 -0700 (PDT), Cosine <ase...@gmail.com>
wrote:
We conducted a test on two groups (A and B). We used aBad reporting. Is the N a total, for equal group sizes?
15-item scale to measure the results. A cut-off score of
6 (scores ranging from 0 to 15, with the higher score being
indicative for stronger reaction) was set to differentiate
the individuals with a clinical reaction from normal individuals.
The null hypothesis is that the two groups have no difference.
The alternative hypothesis is that the reaction of the members
of Group A is greater than that of Group B.
We defined the difference = score of A - score of B.
We chose the alpha = 0.05
We got the following data summarized in the table below.
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -2.10-3.70 400
In addition to the following analysis, what else could we
draw from the data?
Whatever the "cases" are, they are vastly different in SD.
Perhaps Case 1 has scores near zero for all. Or: It will be more
sensible if Case 1 happened to report "Average item score"
whereas the others reported "Scale Total". That would make
the adjusted line for Case 1 read
1 2.25 0.001 0.75-3.75 2000
I haven't done calculations to be sure, but that does
seem like a large SE (on all three) for the reported Ns and
a 15 point scale.
Then too, some numbers have to be wrong. For Case
3, the mean difference is the midpoint of (-1.1, 3.7), not
of the reported (-2.1, 3.7). I assume -1.1 is correct.
But, more seriously, the test results (CI) are inconsistent with
the reported p-values. The SE for each comparison, the
denominator of the t-tests, is about 1/4th the range of the
CI. Using that for a close approximation gives me t-tests of
3.0, 4.94, and 1.08, respectively. The difference for case 2
is clearly the largest, and it is smaller than "p-value = 0.005".
If this is a homework assignment, as Duncan suggests,
Case-1:
P-value < alpha -> significant
95%CI all > 0 -> A > B
Case-2:
the same as those of A
Case-3:
P-value > alpha -> insignificant
95%CI consists of 0 -> not sure if A > B or A < B
you should give credit where credit is due.
--
Rich Ulrich
This has nothing to do with homework or whatsoever.
The table came from Table I of this following paper.
Aarts, S., B. Winkens and M. van den Akker (2012). "The insignificance of statistical significance." European Journal of General Practice 18(1): 50-52.
But the 95% CI of case 3 was printed as: 21.10-3.70.
In addition to the following analysis, what else could we
draw from the data?
How do we determine if the width of the CI is adequate or too wide?
The corrected data of Table I is given below:
Case Mean Difference P-value 95%CI N
1 0.15 0.001 0.05-0.25 2000
2 2.10 0.005 1.25-2.95 1200
3 1.30 0.089 -1.10-3.70 400
For the data provided by the above paper, the author wrote:not rejected. Examples of possible study results, using an ? of 5%, are displayed in Table I. ...
Let us reconsider the above-mentioned hypothetical study. The null hypothesis states that the mean difference between females and males on the GDS-15 (scale ranging from 0 to 15) is zero. Hence, if zero is detected in the 95% CI, the null hypothesis is
Example 2 is not only statistically significant but also clinically relevant; the difference between females and males on the GDS-15 is approximately two whole points. Moreover, the confidence interval is quite
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
narrow, which indicates that the sample size is large enough to make a proper judgement.
^^^^^^^^^
What is the basis for the author to make this judgment?
The author also wrote:
Example 3 is not statistically significant. The confidence interval in this example is very large (almost six
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
points), which makes it difficult to draw any firm conclusions. Since the confidence interval in this
^^^^^^^
Again, why could the author make this statement? What did it mean by almost 6 points?
example includes both negative and positive values, it is not yet clear if there is a difference between these two groups (if females report more depressive symptoms than males or vice versa). Consequently, this study should be repeated using a largersample size, which will decrease the width of the confidence interval.
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