week 7: hypothesis testing

Question 1

Errors in hypothesis testing

Answer 1

Type I errors
Type II errors
Relationship between Type I and Type II errors
Power

Question 2

Type I errors

Answer 2

when the null hypothesis (H0) is actually true

α level

Question 3

Type II errors

Answer 3

when the research hypothesis (H1) is actually true

β

Question 4

Null hypothesis

Answer 4

there is no effect

Question 5

Research hypothesis

Answer 5

there is an effect

Question 6

Statistical significance

Answer 6

if the probability of a score occurring is less than 5% (p < .05), then we interpret that it is unlikely to be due to chance

Question 7

Statistical significance example

Answer 7

we know that the probability of an IQ score being 130 or greater is only 2%

in this case, we would tentatively conclude that the radiation may have had an effect on the person

i.e., We conclude the null hypothesis of no effect is unlikely to explain this score (< 2%) and therefore accept that the research hypothesis of an effect of radiation is a more probable explanation

Question 8

Hypothesis testing

Answer 8

a systematic procedure for determining whether the results of an experiment, which examines a sample that represents the population

Question 9

The process of hypothesis testing

Answer 9

Step 1: formulating research and null hypotheses
Step 2: identifying the comparison distribution
Step 3: determining the cutoff score
Step 4: where does your sample score sit on the comparison distribution?
Step 5: decision time - should the null hypothesis be rejected?

Question 10

Step 1: Formulating research and null hypotheses

Answer 10

think about the objective of the research and restate the research question as:
a research hypothesis about populations
an accompanying null hypothesis about populations

Question 11

Step 1 example

Radiation and intelligence

Answer 11

research hypothesis: radiation exposure improves intellectual functioning
null hypothesis: radiation exposure does not affect intellectual functioning

Question 12

hypothesis formulas

Answer 12

µe > µne this is the research hypothesis

µe = µne this is the null hypothesis

Question 13

radiation IQ example formulas

Answer 13

the IQ of people exposed to radiation will be higher than the IQ of people not exposed
µe > µne this is the research hypothesis
the IQ of people exposed to radiation will be the same as the IQ of people not exposed
µe = µne this is the null hypothesis

Question 14

Step 2: Identifying the comparison distribution

Answer 14

we always test against the null hypothesis (i.e., we assume that there is no difference and we try to find one by showing the chance of no effect is unlikely)
thus, we assume that if the null hypothesis is true:

µe = µne

Question 15

step 2 radiation example

Answer 15

under the null hypothesis, people exposed to radiation will have a similar IQ to those not exposed
we know the characteristics of the distribution of IQ scores in the population (M=100, SD=15)
we test our sample data (the sample statistic) against this distribution specified under the null hypothesis

Question 16

Step 3: Determining the cut-off score

Answer 16

most common is a cut-off of 5% of the distribution
known as the significance level
what is the Z giving us 5%? (z = 1.645)

Question 17

when the obtained score exceeds the critical value

Answer 17

the null hypothesis is rejected

have a statistically significant result

Question 18

Step 4: Where does your sample score sit on the comparison distribution?

Answer 18

find the Z score of your sample result, based on the comparison mean and standard deviation

Question 19

Step 4 IQ radiation example

Answer 19

a person with an IQ of 130 has a Z score of +2 on the distribution of the IQ in the population

Question 20

Step 5: Decision time: Should the null hypothesis be rejected?

Answer 20

is the sample Z score beyond the critical value?
Yes: reject the null hypothesis
No: stay with the null hypothesis (for now)

Question 21

Directional hypotheses

Answer 21

specifies the direction of the difference between the two means
eg. µe > µne

Question 22

Two-tailed tests

Answer 22

it is not known in which direction the difference will lie (eg positive or negative), BUT a difference is hypothesised

Question 23

Cut-off points for two-tailed tests

Answer 23

consider the situation in which a 5% significance level is chosen
need to find cut-off for top 2.5% and bottom 2.5%

Question 24

when is it easier to reject the null hypothesis

Answer 24

it is easier to reject the null hypothesis with a one-tailed test than with a two-tailed test at the same significance level

Question 25

Research Hypothesis

Answer 25

that our IV of interest has had an effect on our DV
this effect can be directional: level 1 will be greater than level 2 or vice versa
i.e., H1: µ1 > µ2 or µ1 < µ2
or no direction: there is a difference but the direction is not specified
i.e., H1: µ1 ≠ µ2

Question 26

Null Hypothesis

Answer 26

is the competing or opposite of the research hypothesis, that there is no effect
i.e., H0: µ1 = µ2

Question 27

critical value or cut-off value

Answer 27

one-tailed: with all 5% in one tail (therefore, a Z score of ±1.64)
two-tailed: with the 5% divided into the two tails producing 2.5% in each tail (thus, a Z score cut-off of ±1.96)

Question 28

whether to reject the NULL hypothesis

Answer 28

• If the sample score is greater than the cut-off (i.e., further out into tails) we reject the null hypothesis and conclude that the IV had an effect on the DV
• If the sample score is less than the cut-off (i.e., closer to the mean) we retain the null hypothesis and conclude that there was no evidence that the IV had an effect on the DV

Question 29

Example

Answer 29

Step1:
Research Hypothesis: Combination Therapy improves depression as measured by MMPI
Null Hypothesis: Combination Therapy has no effect on Depression as measured by MMPI
H1: µT < µNT H0: µT = µ NT
Step 2: Comparison distribution:
Normed distribution of MMPI depression scores of clinical clients (higher score means less depression)
Step 3: Cut-off: 1-tailed Z = 1.645; 2-tailed Z = ±1.96
Step 4: Where does your score sit
Zobt = 2.02 > Zcrit = 1.96
Step 5 Decision: Reject null hypothesis and accept research hypothesise that therapy improved depression.

Question 30

what is significance?

Answer 30

Significance is deciding which distribution

a statistic is more likely to belong to: H0 or H1

Question 31

When we say a result is significant

Answer 31

we are either correct or making a Type 1 error

Question 32

When we say a result is not significant

Answer 32

we are either correct or making a Type 2 error

Question 33

power

Answer 33

the power of a test is its ability to correctly reject the null hypothesis

Question 34

when can power occur

Answer 34

this can only occur when the H1 is true

Question 35

what is power

Answer 35

the power is the area of the H1 distribution which is beyond the critical value on the H0 distribution

Question 36

what type of error is power associated with

Answer 36

power is the ‘complement’ of the Type II error, b

power = 1-b

Question 37

why do researchers like to have lots of power (>.8)

Answer 37

it increases their chances of a correct significant result

Question 38

Power = 1 - β

Answer 38

Probability of finding a significant effect when one

exists in the population