Statistical Inference

Question 1

Why is inferential statistics not practical?

Answer 1

• Not practical to know a population mean because we must infer the mean and error
• Make a conclusion but there is a chance we are wrong

Question 2

What is a population?

Answer 2

Set of all individuals of interest in a particular study

Question 3

What is a sample?

Answer 3

Set of individuals selected from a population
- usually intended to represent population study

Question 4

What is a Parameter?

Answer 4

Value that describes a population

Question 5

What is a parameter derived by?

Answer 5

From measurements of all individuals in the population

Question 6

What is a statistic?

Answer 6

Value that describes a sample

Question 7

What is a statistic derived from?

Answer 7

From measurements of individuals in the sample

Question 8

How do we use sample data?

Answer 8

1. We need to estimate the usual response
2. We need to know how much error is in our estimation

Question 9

What is the best estimation?

Answer 9

Mean +/- Standard deviation

Question 10

How do we estimate error in a sample? Solution #1

Answer 10

Standard deviation correction (see slide 9 for equation)

Question 11

How do we estimate error in a sample? Solution #2

Answer 11

Standard error of the mean (SEM) (see slide 10 for equation)

Question 12

What is standard error of the mean (SEM)?

Answer 12

= the amount of error that may exist when a random sample mean is used to predict a population mean

Question 13

Why are Z scores valuable?

Answer 13

1. Allow us to compare to normal curve
2. Allow us to make predictions
3. Allow us to test hypotheses
4. Allow us to understand the risk of being wrong

Question 14

How to run a thought experiment:

Answer 14

1. Form a hypothesis
2. Collect data in a valid and reliable fashion
3. Find out if our hypothesis is correct
4. Understand how likely we are to be wrong in our conclusion

Question 15

What to do when forming a statistical hypothesis

Answer 15

Create two mutually exclusive and exhaustive mathematical statements about the outcome of the analysis

Question 16

What is a mutually exclusive statement?

Answer 16

Only one of the two can be true

Question 17

What is an exhaustive statement?

Answer 17

No other option can exist

Question 18

What is the statistical significance?

Answer 18

• This decision of significance is based on the probability that you might be wrong
• The degree of risk you are willing to take to reject the null hypothesis when it is actually true

Question 19

What is the significance level?

Answer 19

Risk associated with not being 100% positive that what occurred in the experiment is a result of what you did or what is being tested

Question 20

What is the most commonly used level of confidence?

Answer 20

p < 0.05 (5% chance that you reject the null hypothesis when it’s actually true)
- 95% confident

Question 21

What is Type I error (False positive)

Answer 21

The probability of rejecting the null hypothesis when it’s true (alpha level a)

Question 22

What conventional level s alpha usually set between?

Answer 22

0.01 and 0.05

Question 23

What is Type I error caused by?

Answer 23

• measurement error
• lack of random sample
• alpha too liberal (0.10)
• investigator bias
• improper use of 1 tailed test

Question 24

What is Type Ii error (False negative)

Answer 24

Probability of accepting a null hypothesis when it’s false (beta level b)
- more difficult to control than type I

Question 25

What is b level often set to?

Answer 25

0.20 (20%)

Question 26

What is type II error caused by?

Answer 26

• measurement error
• low power (N too small)
• alpha too conservative (0.01)
• treatment effect no properly applied

Question 27

How to draw a conclusion

Answer 27

State the result, your conclusion, and the degree of confidence you have in this conclusion (p value)