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Old 04-21-2011
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Stats Biostatistics Question: Analyzing these groups

Researchers wish to determine the efficacy of a new weight loss regimen. To do this, they compare the amount of weight loss by 40 patients on the regimen (Group A) with 40 people selected at random from a commercial weight loss program (Group B) and 30 volunteers who were trying to lose weight on their own (Group C). Results of weight loss study are shown below :

Group A
Mean : 17.3 lb, SE : 3.4, N : 40

Group B
Mean : 12.7 lb, SE : 4.3, N : 40

Group C
Mean : 5.4 lb, SE : 5.3, N : 30

SE = standard error, N : sample size

Based on the results above and using a criterion level of p<0.05, the researchers are most likely to conclude that :

A. Group A lost more weight than Group B and Group B lost more weight than Group C.
B. Group A showed more weight loss than Group C, but not more than Group B.
C. Group A showed significantly more weight loss than either of the other two groups.
D. No answer is possible without the results of statistical test being given.
E. No significant differences were found among the three groups.
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Old 04-21-2011
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I would say B: Group A showed more weight loss than Group C, but not more than Group B.

The SEs overlap in Group A and B (meaning group A has a range of 13.9-20.7 whereas Group B has a range of 8.4-17.0), so no difference there, but Group A doesn't overlap with the values in C.

I always mix up SE and SD; I know you can use the SD to reason through this like i just did, but is that correct to use the SE that way?
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I was thinking B, but also have the same question about SE vs SD
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This is a good question to test your concept on Standar Deviation, Standard Error and Confidence Interval, that's why I post it here. It can be very tricky. I will wait for more responses.
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I'm inclined to say D
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Quote:
Originally Posted by 1TA2B View Post
I'm inclined to say D
D sounds enticing, but it's probably a cop out answer choice like the answer choices in bioethics that say "refer to ethics committee" or "go to court"
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Quote:
Originally Posted by apx85 View Post
D sounds enticing, but it's probably a cop out answer choice like the answer choices in bioethics that say "refer to ethics committee" or "go to court"
lol I agree! Plus I wouldn't say NO answer is possible; you can't conclude statistical significance if you don't have the results of a statistical test, but you can conclude something if you want to.
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Iam going with C
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I would say D

Strictly speaking, we should do an ANOVA (calculated SSB & SSW) and then a post hoc analysis.
With the ANOVA, the only conclusion would be "at least one mean group is different", but then, with a post hoc (i.e. bonferroni), we would have to compare A&B, B&C and A&C (the type one error should be correct it)
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We have various answers here, unfortunately no one hit the correct one.

Although p value is not mentioned above, we can still conclude the statistical significance of this study by computing confidence interval from each group.

The question set the the criterion level of p <0.05, so we must compute 95% confidence interval.

95% CI = mean +/- (z x SE)
z score for 95% CI is 2

For group A :
95% CI = 17.3 +/- (2 x 3.4)
= 17.3 +/- 6.8
= 10.5 to 24.1

Using the same formula
For group B :
95% CI = 4.1 to 21.3

For group C :
95% CI = -5.2 to 16

The confidence interval of each group is overlapping to each other, thus we can conclude that there were no significant difference among three groups (E)
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Quote:
Originally Posted by harlesmd View Post
We have various answers here, unfortunately no one hit the correct one.

Although p value is not mentioned above, we can still conclude the statistical significance of this study by computing confidence interval from each group.

The question set the the criterion level of p <0.05, so we must compute 95% confidence interval.

95% CI = mean +/- (z x SE)
z score for 95% CI is 2

For group A :
95% CI = 17.3 +/- (2 x 3.4)
= 17.3 +/- 6.8
= 10.5 to 24.1

Using the same formula
For group B :
95% CI = 4.1 to 21.3

For group C :
95% CI = -5.2 to 16

The confidence interval of each group is overlapping to each other, thus we can conclude that there were no significant difference among three groups (E)
Good Job! Thanks.

A couple of queries!

1. How do you get "2"?

2. What is the relationship between standard deviation and standard error?" It looks like SD equals -muliplies "z" of SE.
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Quote:
Originally Posted by harlesmd View Post
We have various answers here, unfortunately no one hit the correct one.

Although p value is not mentioned above, we can still conclude the statistical significance of this study by computing confidence interval from each group.

The question set the the criterion level of p <0.05, so we must compute 95% confidence interval.

95% CI = mean +/- (z x SE)
z score for 95% CI is 2

For group A :
95% CI = 17.3 +/- (2 x 3.4)
= 17.3 +/- 6.8
= 10.5 to 24.1

Using the same formula
For group B :
95% CI = 4.1 to 21.3

For group C :
95% CI = -5.2 to 16

The confidence interval of each group is overlapping to each other, thus we can conclude that there were no significant difference among three groups (E)
Actually this is not quite correct. You can calculate each 95CI%, but since u are doing 2 comparisons, you increased your alpha error (this error follows a binomial distribution). I know that this may sound a little bit technical...but this is way we use ANOVA and we donīt do multiple t test or multiple 95CI%....

the number 2 is just an aprox. of Z alpha (normal dist) two sided tail (2.5%each side =1.97).
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Definitely you can confirm this result with ANOVA test, and calculating the f value (for ANOVA test, you don't need to do it manually, you can use the software) and again the p value will be > 0.05 (not statistically significant). Thus choosing option D won't be the best answer.
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Quote:
Originally Posted by harlesmd View Post
Definitely you can confirm this result with ANOVA test, and calculating the f value (for ANOVA test, you don't need to do it manually, you can use the software) and again the p value will be > 0.05 (not statistically significant). Thus choosing option D won't be the best answer.
hahaha...I know that...and u also can do multiple t test with corrections or permutations. The all point is the concept....In this case was pretty obvious the answer, but the concept is wrong ...and u can do it manually, trust me, haha
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Quote:
Originally Posted by bebix View Post
hahaha...I know that...and u also can do multiple t test with corrections or permutations. The all point is the concept....In this case was pretty obvious the answer, but the concept is wrong
Sorry but I didn't really get your point. Which concept is wrong ?
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Quote:
Originally Posted by harlesmd View Post
Sorry but I didn't really get your point. Which concept is wrong ?
I really don't want to confuse people here, so I sent u a PM with a simulation.
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