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Old 05-12-2011
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Stats The Zero value in Confidence interval?

Hello USMLE friends

I have a real trouble understanding questions about the error type 1 and type 2 and confidence interval

for example when they say " The confidence interval includes 0, meaning that the null hypothesis (no difference between operative and nonoperative patients) cannot be rejected. Because this researcherís conclusion incorrectly accepts the alternative hypothesis (H1), he has committed a Type 1 error"

A Type II error would involve failing to reject the H0 (i.e., there is a difference but the researcher didnít find it). which mean the confidence interval included 1

how can I know that there is a O or 1 in the confidence interval?

for example I found a question with (95% CI: -2% to 12%) and in the answer they said that this CI include 0 ??

any help please ?
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Old 05-16-2011
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Imagine this scenario:

H0: A new treatment is not more effective than the traditional one
HA: A new treatment is more effective than the traditional one


The 4 options are:

1. Adopt the new treatment when in reality the new treatment is more effective = Correctly rejecting the null hypothesis - Power
2. Continue with the traditional treatment when in reality the new one is more effective = Type II Error - the event that the null is not rejected when the alternative is true
3. Continue with the traditional treatment when in reality the new one is not more effective = Correctly not rejecting the null hypothesis
4. Adopt the new treatment when in reality the new one is not more effective = Type I Error - the event that the null hypothesis is rejected when H0 is actually true

Now, in statistics, the test statistics is always under the null (H0):
1.- When we are talking about the difference in proportions between group A & B OR the difference in means between group A & B, our test statistic follows H0 = where the null value equals zero
2.- When we are comparing Odds Ratio/Risk Ratio, again our test statistic follows H0, but this time the null value would be equal to one (OR or RR = 1 under the null).
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Old 05-16-2011
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Quote:
Originally Posted by bebix View Post
Imagine this scenario:

H0: A new treatment is not more effective than the traditional one
HA: A new treatment is more effective than the traditional one


The 4 options are:

1. Adopt the new treatment when in reality the new treatment is more effective = Correctly rejecting the null hypothesis - Power
2. Continue with the traditional treatment when in reality the new one is more effective = Type II Error - the event that the null is not rejected when the alternative is true
3. Continue with the traditional treatment when in reality the new one is not more effective = Correctly not rejecting the null hypothesis
4. Adopt the new treatment when in reality the new one is not more effective = Type I Error - the event that the null hypothesis is rejected when H0 is actually true

Now, in statistics, the test statistics is always under the null (H0):
1.- When we are talking about the difference in proportions between group A & B OR the difference in means between group A & B, our test statistic follows H0 = where the null value equals zero
2.- When we are comparing Odds Ratio/Risk Ratio, again our test statistic follows H0, but this time the null value would be equal to one (OR or RR = 1 under the null).
thank you so much for the great explanations. I wan't to understand this
you said " When we are talking about the difference in proportions between group A & B OR the difference in means between group A & B, our test statistic follows H0 = where the null value equals zero "
so if 0 is include within the 2 variable; so H0 is not rejected? so this mean that there is no difference. I'm I right?
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Old 05-16-2011
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When we have 2 groups and we calculate a 95% CI for the diff. in means between groups

[-10,10] = the null value is included in the CI = you fail to reject H0 (no difference)
[0.001, 10] = the null value is not included in the CI = you reject H0
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Old 05-16-2011
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Quote:
Originally Posted by bebix View Post
When we have 2 groups and we calculate a 95% CI for the diff. in means between groups

[-10,10] = the null value is included in the CI = you fail to reject H0 (no difference)
[0.001, 10] = the null value is not included in the CI = you reject H0
Oh thank you very much it's more clear now!!
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Old 07-28-2014
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Default Confidence Interval Doesn't contain zero

So the statistical question I have is, "If an 85% confidence interval (CI) for the difference between two population groups is as follows:

-15.8% < Pa-Pb <-7.9%

Is there a significant difference between these population percentages.

My thought was that since the CI does NOT contain zero then I can conclude that there IS a significant difference at the 1-.85 = 15% level. However, the question is T/F. Would you conclude there IS a significant difference regardless of the CI, based completely on the fact that it does not contain zero? This doesn't seem correct to assume a significant difference independent of the CI level.
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