Null hypothesis tests

Question 1

Hypothesis testing

Answer 1

Alternative method for making inferences on population
Start with a default assumption (null hypothesis) and see if the evidence from sample is strong enough to reject it

Question 2

Null hypothesis

Answer 2

Some null or conservative stat (assumption made without evidence to the contrary)

○ E.g. H0 is that Australian students are no different from American students
In treatment studies, H0 will be that the treatment is the same as the control

	○ If M is consistent with µ =  µ0 then we reject H0

Question 3

How to determine if you reject or retain H0

Answer 3

Null hypothesis is retained unless there is evidence to the contrary
The accused is presumed innocent unless the evidence shows guilt beyond reasonable doubt

Question 4

Level of significance

Answer 4

Ways to determine that the null hypothesis is implausible (unlikely value of M)
Determined by the amount of error the experimenter is will to tolerate, expressed as a probability

• Reflects the fact that when estimating a parameter from a sample statistic (µ from M) its impossible to eliminate error only to quantify the likelihood of error
• ‘a’ is set at 0.05 by convention by sometimes other values are used e.g. 0.01

Question 5

Type 1 error

Answer 5

Rejecting the null hypothesis when it is actually true (false alarm) - regarded as worse

(Saying there is an effect where there isn’t)

Question 6

Type 2 error

Answer 6

Retaining a false H0 (misses)

(Saying there is no effect when there is)

Question 7

Why cant you have a super small alpha

Answer 7

Alpha is a way of controlling the risk of making Type I error
- A very small alpha would minimise the risk of Type I errors (e.g. a = 0.001 means incorrectly rejecting H0 only 0.1%)
- But if the H0 is actually false it is harder to reject with a small alpha = increasing risk of Type II error

Question 8

Experimental hypothesis

Answer 8

Experimenter will predict something positive e.g. new treatment is effect so they are hoping to reject the H0 and get a significant result
- But sometimes they might predict a null result so they would be hoping to retain the H0

Question 9

What is a one-tailed test

Answer 9

• Directional!

Used when an effect in the opposite direction to H1 would be of no interest

Effects that are significant with a one-tailed but not with a two-tailed criterion are viewed with suspicion among researcher