QM LM8 Hypothesis testing

Question 1

What is statistical inference?

Answer 1

The process of making judgements about a larger group (population) based on a smaller group (sample)

Question 2

What is hypothesis testing?

Answer 2

Testing to see whether a sample statistic is likely to come from a population with the hypothesised value of the population parameter
This is statistical inference

Question 3

What is a hypothesis?

Answer 3

A statement about one or more populatiosn that are tested using sample statistics

Question 4

What is the process of hypothesis testing, in 6 steps?

Answer 4

1. State the hypothesis
2. Identify the appropriate test statistic
3. Specify the level of significance
4. State the decision rule
5. Collect data and calculate the test statistic
6. Make a decision

Question 5

What is the null hypothesis?

Answer 5

Something we assume to be true unless we can reject it
- Typically, we WANT to reject the null
- However there are some cases in multivariate testing where we want the null.

Question 6

What is a two tailed test?

Answer 6

• For example, the null hypothesis might be that mu = 6%
• The value might be greater or less than 6%
• It can be not equal in both directions

Question 7

What is a one tailed test?

Answer 7

• For example, where the null hypothesis that mu is less than 6%
• Here, when the mu is close to or above 6% we reject the null
• Therefore there is a rejection outcome on only one side of the distribution

Question 8

If the population variance is unknown, what kind of test statistic do we use?

Answer 8

• T-test by default, because it is stricter than a z-test
• If the T-test allows us to reject the null, we will CERTAINLY be able to reject the null under a z-test as well

Question 9

What level of significance should we use?

Answer 9

• Depends on the seriousness of making a mistake
• In social sciences we might use 10%
• In finance we use 5% as standard, maybe 1%
• The greek shorthand is alpha

Question 10

What are the two types of mistake we could make when doing hypothesis testing?

Answer 10

• If the null is rejected and happens to be true (false positive). E.g., telling someone they’re pregnant when they’re not.
• If the null is not rejected and happens to be false (false negative). E.g., telling someone they’re not pregnant when they are

Question 11

How does decreasing the level of significance affect type II errors?

Answer 11

• As alpha decreases (level of sig), beta increases
• Beta is the likelihood of type II error. This is a false negative: failing to reject the null hypothesis when the null should be rejected (telling someone they’re not pregnant when they are)
• The only way to decrease both alpha and beta (decrease false psitives AND false negatives) is to increase n (the number of observations)

Question 12

What is 1 - beta?

Answer 12

The power of the test
The ability to reject the null hypothesis when it should be rejected

This is contrasted to 1 - alpha, which is the significance level

Question 13

Do we test standard deviation or variance?

Answer 13

• We always test variance, not SD
• We use chi squared test to test variance
• since variance cannot be negative we can’t use a z-test

Question 14

When would you use parametric testing?

Answer 14

• When sample statistics are being used to test population parameters
• However our data has to meet distributional assumptions, for example follow an approximately normal distribution

Question 15

When would you use non-parametric testing?

Answer 15

1. When there are no parameters tested
2. When there are no distributional assumptions

• I.e., if n<30 the population is non-normally distributed
• When there are outliers, we might test for median rather than mean (so use non-parametric)
• When data are given in ranks, or used an ordinal scale (ordered or categorical)
• When the hypothesis does not concern a parameter (i.e., testing if a sample is random)

Question 16

Under what circumstances must we NOT use a t-test?

Answer 16

• If n<30 AND it’s non-normal
• If it’s non-normal we cannot use parametric tests (based on parameters) we must use non-parametric tests
• If n >40 we can use either z or t-test

Question 17

How do you tell whether you are doing a left-tailed or right-tailed test?

Answer 17

• Look at the way the < or > sign is pointing
• We all know the crocodile eats the bigger number
• However, we can also see it as an arrow
• The arrow points right, it is a right-tailed test
• The arrow points left, it is a left-tailed test

Question 18

How do you read a t-table?

Answer 18

• Determine the number of degrees of freedom (n - 1 of your sample)
• This is because t distributions are different depending on degrees of freedom
• Then read across the table and find the critical value based on how much is left in each tail
• (1% level two-tailed test we would have to look at the 0.005 column)

Question 19

What is an F-test?

Answer 19

• The ratio of two chi-square variables
• Each one has chi square degrees of freedom
• Whichever is larger is the numerator

Question 20

Do we use left or right tailed tests for chi square variables?

Answer 20

• We can use either left or right tail, but we always test to the right of the line

Question 21

How do you use an F-table?

Answer 21

• Find the larger degrees of freedom of your two chi squared values, read down the column
• Find the smaller degrees of freedom and read across
• The number in that cell will be the critical value