Making Decisions

Question 1

What is a z score in this context?

Answer 1

A measure of distance between the sample statistic and the population parameter
Consult normal tables to decide the exact probability that the sample subgroup has the same mean as the pop

Question 2

Z scores and critical values

Answer 2

5% - critical zone is equal to or exceeding -+ 1.96
We reject the null hypothesis when the z score is equal to or exceeds this

Question 3

How do we formulate hypotheses?

Answer 3

Null hypothesis - The mean is not different from the mean of the population
Alternative hypothesis - The mean is different from the mean of the population

Question 4

Why do we not increase the level of significance?

Answer 4

This would increase the number of times we accept the null hypothesis when we should actually reject it

Question 5

What is a type 1 and a type 2 error when hypothesis testing?

Answer 5

A type 1 (Alpha) error - where you reject the null hypothesis and accept the alternative hypothesis but null is true
A type 2 error (beta) - where you fail to reject the null hypothesis but the null hypothesis is not true

Question 6

Testing the null hypothesis

Answer 6

We test the null hypothesis we do not prove it
Accept or reject
We can also use CI for hypothesis testing

Question 7

What is the difference between 2 tailed test or 1 tailed ?

Answer 7

2 tailed - normal way - non directional - we reject the null hypothesis if the sample statistic reaches the critical value in either tail
1 tailed - any association can only be in one direction we allocate the risk to just one side (directional)

Question 8

How do we decide which test to use?

Answer 8

Pop SD is known - Z test
Pop SD is not known - sample size is greater than 30 - Z test
Pop SD is not known - sample size is less than 30 - Normally distributed - t test
Skewed - Sign test

Question 9

How do we decide if the distribution is normal?

Answer 9

Look at histograms
Check SPSS output for skewness and kurtosis - for 5% does zskew or zkurt equal or exceed -/+ 1.96

Question 10

Skewness

Answer 10

Scores are bunched up on one side and trail to the other
We use the median

Question 11

Kurtosis

Answer 11

A measure of how peaked or flat the distribution is
Platykurtic - Flat
Leptokurtic - Very peaked

Question 12

How do we calculate Zskew and Zkurt?

Answer 12

Zskew - skewness / std error of skewness
Zkurt - Kurtosis / std error of kurtosis