Stats- C9

Question 1

What are the qualities of a good sample?

P51

Answer 1

Previous chapters discussed the analysis method. However for answering the research question we need the proper data as well. A good sample is
1. Sufficient (enough data so the patterns you see are likely to be real)
2. Relevant (the data will help you the problem you will try to solve)
3. Representative (the full range of actual process conditions)
4. Contextual(collected along with other information to make connections)
5. NOT biased
6. NOT isolated
7. balanced (not too many missing values)

Best practise is to determine the required sample size for a test with a required power. P53

Question 2

What is type II error?

Answer 2

β Is the probability of wrongly failing to reject the hypothesis (False-negatives). Examples of type II errors: We would state that It’s a Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does (we fail to detect the difference). A cancer patient believes the experimental drug has a 75% cure rate when it has a cure rate that is less than 75% (we fail to reject H0 hypothesis). Type II errors can lead to rather serious errors, influencing conclusions of the research.
schema

Question 3

Selection of an appropiate sample size is one of the most important aspects of any experimental design problem. Whether we have enough data we assess by the ____

P51

Answer 3

Power of the test

Question 4

The ”power of the test” is calculated by the type error II β as
____ ,where β is the probability of wrongly failing to reject the hypothesis (False-negatives).

P52

Answer 4

1 − β

Question 5

Suppose we are testing the hypothesis
H0 : µ1 = µ2
Ha : µ1 != µ2
and that the means µ1 and µ2 are not equal so that δ = µ1−µ2. Because H0 : µ1 = µ2 is not true (µ1 and µ2 are not equal ) we are concerned about wrongly failing to reject the H0 hypothesis.
The bigger δ the ____ (more/less) likely we fail to reject the hypothesis, In other words, the probability of the type II error β depends on the true difference of means δ.

P52

Answer 5

less
Ref

Question 6

The sample size is important, as for a given value δ, the β error ____ (decreases/Increases) as the sample size increases.

P52

Answer 6

Decreases

Question 7

What’s the power of a test?

Answer 7

The power of a hypothesis test is the probability that the test correctly rejects the null hypothesis (H0) when a specific alternative hypothesis (Ha) is true. (1-typeII error)

Question 8

Properly designed experiments must ensure that power will be reasonably high to detect reasonable departures from the null hypothesis. Otherwise, an experiment is hardly worth doing. A rule of thumb is that the power of a test should be > ____.

Answer 8

0.8

Question 9

Factors that influence the power: (4)

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Answer 9

1. Kind of the statistical test that’s being performed. Some statistical tests are inherently more powerful than others.
2. Sample size n. In general, the larger the sample size, the larger the power. However, generally increasing sample size involves tangible costs, both in time, money, and effort. Consequently, it is important to make sample size ”large enough,” but not wastefully large.
3. The size of experimental effects δ (Me: δ = µ1 −µ2 P51) . If the null hypothesis is wrong by a substantial amount, power will be higher than if it is wrong by a small amount.
4. The level of error in experimental measurements SE. Measurement error acts like ”noise” that can bury the ”signal” of real experimental effects. Consequently, anything
   that enhances the accuracy and consistency of measurement can increase statistical power.

Question 10

Sample Size Calculations

P53

Question 11

Power of a test

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