Hypothesis Testing

Question 1

Inferential statistics and what it comprises of

Answer 1

Process of using samples to make inferences about a population example t-tests
Confidence interval
And hypothesis testing ( a significance test)

Question 2

Hypothesis testing

Answer 2

Test a specific hypothesis using sample data to decide on validity of hypothesis also called significance testing

Question 3

What does hypothesis testing involve

Answer 3

Setting up 2 opposing hypothesis concerning a parameter in the population
Sampling the population and extracting evidence from the resulting sample data
Making judgement as to which hypothesis is best supported by the evidence

Question 4

Statistical hypothesis

Answer 4

A statement about a parameter or distribution of a population being sampled (an assumption that may or may not be true concerning 1 or more populations)

Question 5

Null hypothesis vs alternative hypothesis

Answer 5

Null hypothesis is the specific aim being tested (we hope to reject in evidence in our data)
Alternative hypothesis the claim about the population that we suspect to be true ( evidence in favor of this claim)

Question 6

Types of alternative hypothesis

Answer 6

One sided direction: parameter is larger than or smaller that null hypothesis value
Two sided : parameter is different null value it could be less or more

Question 7

Notes about null and alternative hypothesis

Answer 7

Are always stated in terms of population parameters or distribution

Question 8

Test statistic or estimator

Answer 8

Quantity calculated from sample to measure how much the observed sample data differ from what we would expect to see if null hypothesis were true

Question 9

What does a large statistic value mean

Answer 9

Means sample data is different than data that we would expect to see under the null hypothesis so unlikely that null hypothesis is true

Question 10

P value of a test

Answer 10

Probability that test statistic would have a value as extreme or more extreme than the value actually observed if the null were true
It’s a probability so lies between 0-1

Question 11

What does a small p value mean

Answer 11

There is stronger evidence against null hypothesis

Question 12

When making a decision we either

Answer 12

Reject the null or fail to reject the null

Question 13

Significance level what happens when p value is less that alpha

Answer 13

Decisive value that we compare p value to (denoted as alpha)
Is p value from our data is less that alpha we reject null hypothesis
Alpha =0.05
But depending on question it may be 0.01, 0.10

Question 14

Critical value

Answer 14

Critical value of test statistic is cut off value that corresponds to given significance level which is determined from probability distribution of test statistic
If the observed test statistic value is as extreme or more extreme than c we reject null hypothesis

Question 15

When we reject null hypothesis we say?

Answer 15

Result is statistically significant

Question 16

Type 1 error and type 2 error

Answer 16

Type 1 - rejecting null hypothesis when it is true(rejection error)
Type 2- not rejecting the null hypothesis when it is false or failing to reject null when alternative is true
(Acceptance error)

Question 17

How can you reduce type 1 and type 2 errors

Answer 17

Increasing sample size

Question 18

High power

Answer 18

Power is the ability of statistical test to reject null when null is false usually a power of 80-90% is desirable , increasing power makes type 2 error rate low

Question 19

To calculate sample size when comparing 2 means you need 4 quantities

Answer 19

1. An estimate of population standard deviation
2. Smallest difference between 2 groups
3. Significance level alpha
4. Probability 1- type 2 error (beta)

Question 20

For independent observation that formula give vale of z alpha and beta

Answer 20

Z alpha= 2.58 for alpha =0.01
1.96 for alpha =0.05

Z beta =0.84 for 80% power
1.28 for 90% power

Question 21

Relationship between sample size and other factors

Answer 21

Required sample size increases as
1.Power increases
2. Effect size decreases
3. Variance increases
4. Significance level decreases

Question 22

A hypothesis test may be statistically significant but not practically meaningful true or false

Answer 22

True

Question 23

Reasons for When a test is not statistically significant

Answer 23

Null hypothesis is true or
We did not have the power to detect a departure from the null due to low sample size