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#1
05-18-2011
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,357 Threads: 194 Thanked 3,259 Times in 881 Posts Reputation: 3269
Type I and II error and Power

For each of the following situations, using statements 1 through 4, identify which is the Type I Error, Type II Error, the event of correctly rejecting the null hypothesis (Power) and the event of correctly not rejecting the null hypothesis.

Null Hypothesis: A production run of a drug is of satisfactory quality
Alternative Hypothesis: A production run of a drug is of unsatisfactory quality

Conclusions of the study:

1. Reject a run of satisfactory quality.
2. Put on the market a run of satisfactory quality.
3. Reject a run of unsatisfactory quality.
4. Put on the market a run of unsatisfactory quality.

a) Type I error
b) Type II error
c) Power
d) Correctly not rejecting the null hypothesis.
 The above post was thanked by: Claus_CU (05-18-2011), doc_study (05-18-2011), struggle (05-18-2011)

#2
05-18-2011
 USMLE Forums Guru Steps History: Not yet Posts: 324 Threads: 70 Thanked 236 Times in 143 Posts Reputation: 246

1. Type I error (rejecting null hypothesis)
2. Correctly not rejecting the null hypothesis.
3. Type II error (not rejecting null hypothesis)
4. Power
That's what i think..
 The above post was thanked by: bebix (05-18-2011)
#3
05-18-2011
 USMLE Forums Scout Steps History: Step 1 Only Posts: 82 Threads: 8 Thanked 114 Times in 49 Posts

My guess...

1. a) Type I error
2. d) Correctly not rejecting the null hypothesis.
3. c) Power
4. b) Type II error
__________________
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 The above post was thanked by: bebix (05-18-2011), struggle (05-18-2011)
#4
05-18-2011
 USMLE Forums Addict Steps History: 1 + CS Posts: 113 Threads: 8 Thanked 88 Times in 61 Posts Reputation: 98

1- a
2- d ?
3- c
4- b
#5
05-19-2011
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,357 Threads: 194 Thanked 3,259 Times in 881 Posts Reputation: 3269

1. Reject a run of satisfactory quality => a) Type I Error - the event that the null hypothesis is rejected when H0 is actually true

2. Put on the market a run of satisfactory quality => d) Correctly not rejecting the null hypothesis

3. Reject a run of unsatisfactory quality => c) Correctly rejecting the null hypothesis - Power

4. Put on the market a run of unsatisfactory quality => b) Type II Error - the event that the null is not rejected when the alternative is true
 The above post was thanked by: struggle (05-19-2011)
#6
05-19-2011
 USMLE Forums Guru Steps History: Not yet Posts: 324 Threads: 70 Thanked 236 Times in 143 Posts Reputation: 246

can you please explain option 3 and 4 in detail. I actually didn't get it. :sorry:
#7
05-19-2011
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,357 Threads: 194 Thanked 3,259 Times in 881 Posts Reputation: 3269

Quote:
 Originally Posted by struggle can you please explain option 3 and 4 in detail. I actually didn't get it. :sorry:

Null Hypothesis: A production run of a drug is of satisfactory quality
Alternative Hypothesis: A production run of a drug is of unsatisfactory quality

3. Reject a run of unsatisfactory quality => c) Power
Power = P( reject H0 | H0 NO TRUE ) = P( reject H0 | HA is TRUE )= 1 - Beta
Power = P( reject "A production run of a drug is of satisfactory quality" | "A production run of a drug is of unsatisfactory quality")
= Reject a run of unsatisfactory quality

4. Put on the market a run of unsatisfactory quality => b) Type II Error
Type II = P( not reject H0 | HA true ) = P( "accept" H0 | HA true) ** we never "accept" H0, we just reject or fail to reject it…but I wrote it like that for a better understanding
Type II = P( fail to reject "A production run of a drug is of satisfactory quality" | "A production run of a drug is of unsatisfactory quality" )
= Put on the market a run of unsatisfactory quality (we put it on the market anyway)

* P(x|y) = the probability of some event x, given the occurrence of some other event y
 The above post was thanked by: Claus_CU (06-09-2011), samstar (07-16-2011)

 Tags Biostatistics-Epidemiology, Step-1-Questions

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