MMB-Stats_2_SignificanceTesting

Question 1

1. Discuss Karl Popper’s paradigm state.

Answer 1

• Popper taught that science is about hypothesis testing. It advances by making hypotheses, testing them, rejecting them, and coming up with better hypothesis, testing these, etc. etc.
• He was opposed to the more traditional view that science proceeds by induction, ie generalising from particular observed instances.
• This philosophy affected science profoundly, not always for the good. In practice, science needs to have an exploratory aspect as well as a confirmatory, hypothesis-testing mode.

Question 2

2. What di the ideas of R A Fisher give experimental psychology?

Answer 2

• R A Fisher designed statistical tests which happened to fit Popper’s philosophy, and in effect made it possible for experimental psychologists to ‘operationalise’ Popperism.

Question 3

3. Give a clear example of how Fishers model works using a double negative.

Answer 3

Fisher’s idea was to get around the difficulties with induction by essentially proving something using a double negative. The very basic logic behind this can be illustrated by the following trivial example.

• Suppose I want to prove that “the earth is not flat”. I assume the opposite, “the earth is flat”. I then derive various conclusions that follow logically from this, among which is “anyone going far enough will fall off the edge”. But I know that that is not true: the experiment has been done, and you don’t fall off the edge. Therefore, the earth is not flat.

Question 4

4. How is an experiement designed in the way Fisher defined?

Answer 4

We design an experiment to gather data to test the null hypothesis, which we hope will give a result which leads us to reject the null. The way we do this is to look for a region of possible data outcomes which is improbable if the null hypothesis is true. We usually, following Fisher, take a region with a probability of only 1 in 20, or 5%, given the null hypothesis.

Question 5

5. Define null hypotheis.

Answer 5

The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance.

Question 6

6. What does NHST stand for?

Answer 6

Null Hypothesis Significance Testing

Question 7

7. Can a Null Hypothesis ever be accepted?

Answer 7

A null hypothesis can be rejected if the data is surprising (has a probability below some arbitrary limit, usually 0.05), but it is never accepted if the reverse is true: we merely fail to reject it on the current evidence.

Question 8

8. Define type 1 error

Answer 8

A type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. With respect to the non-null hypothesis, it represents a false positive. Usually a type I error leads one to conclude that a supposed effect or relationship exists when in fact it doesn’t.

Question 9

9 Define the Z test

Answer 9

A statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed.

Question 10

10. Define a T Test.

Answer 10

A statistical examination of two population means. A two-sample t-test examines whether two samples are different and is commonly used when the variances of two normal distributions are unknown and when an experiment uses a small sample size. For example, a t-test could be used to compare the average floor routine score of the U.S. women’s Olympic gymnastic team to the average floor routine score of China’s women’s team.