Hypothesis Testing and

Inferential Statistics

Chapter 7

Ethnic differences in clinical dissociation

Dissociative Experiences Scale (DES)

Psychological defense mechanism for victims of traumatic events

Detach themselves from trauma so loose consciousness, memory, identity or perception

Overall population M = ~18.5

Douglas (2003)

Examine minorities’ scores on the DES

Hypothesis: minorities’ scores higher (more dissociations) compared to population scores

Hypothesis Testing

State hypothesis about a population

Predict characteristics of sample (mean, SE)

Obtain sample data

Compare sample data with prediction

Does “treatment” have an effect?

Make decision based on probability of getting

that result given a particular population

Write conclusion

Hypothesis Test

2 hypotheses

Null hypothesis = H0: µ0 = µ1

No difference between groups

No effect of IV

Alternative hypothesis = Ha or H1: µ0 ≠ µ1 Treatment or condition has effect

Direction of H1: increase, decrease or both

Criteria… is it “significant”? Set alpha level or probability

Usually = .05

Result not likely due to chance

Testing the Null Hypothesis

“Presumed innocent until proven guilty”

We do NOT test the research (alt) hypothesis directly; we test the null hypothesis

Stats better at showing something is not true; so try to falsify the null hypothesis

Assume that differences are due to normal variability expected in a population

The more variability in population the harder to reject null hyp

Use statistics to reject null hypothesis or not Is difference too great to happen by chance?

Since can’t test alternative hypothesis directly Can never PROVE that it is correct

Can only find support for it

Hypothesis testing

Critical region

Region of rejection

Defines “unlikely event” for H0

distribution

Alpha ( )

Probability value for critical region

If set .05 = probability of result

occurred by chance only 5x out of 100

Critical value (cv)

Value of the statistic for alpha

p-value

Actual probability of result occurring

Inferences drawn from statistics

Test hypothesis with “test statistic”

z-scores (for now…)

Examine if obtained difference is different than what is expected by chance

When you reject the null hypothesis:

“The findings are statistically significant.”

When you fail to reject the null hypothesis:

“There was no evidence found that…”

When you find p = .06 (for = .05)

“A marginally significant result was found.”

Direction of prediction

Two-tailed test

Non-directional hypothesis

H0: µ = 0

H1: µ ≠ 0

One-tailed test

Directional hypothesis

Predict increase or decrease

H0: µ = 0

H1: µ < 0 OR µ > 0

Which do you choose?

What alpha do you choose?

Alpha level: 2-tailed test

-3 -2 -1 0 1 2 3

-3.30 +3.30 +2.58 +1.96 -1.96 -2.58

= .05

= .01

= .001

zcv scores

Alpha level: 1-tailed test

-3 -2 -1 0 1 2 3

+3.09 +2.32 +1.645

= .05

= .01

= .001

zcv scores

Ethnicity differences in clinical dissociation

Dissociative Experiences Scale (DES)

Two-tailed or one-tailed test?

Null hypothesis (H0)

µ0 = µ1

Alternative hypothesis (H1)

µ0 < µ1

Results (means only):

Majority Af-Amer Asian Latino

18.50 22.45 19.67 21.55

Inferential statistic: z-test

Z-score: Comparison of score with population distribution in terms of SD from population mean

Sampling distribution’s µx = µ

σx < σ

Standard error of mean = σx= σ/√N

Z-test: Comparison of sample mean with sampling distribution

( )X

X

xz

50 100 150

0.00

0.01

0.02

0.03

IQ

Den

sity

IQ for 1 Subject

1151059585

80

70

60

50

40

30

20

10

0

Mean IQ for 10 Subjects

Fre

qu

en

cy

N

Mz

Ethnicity differences in clinical dissociation

Calculate z-test for sample mean

If µ = 18.5

If σ = 6

If M = 22.5

If N = 20

Conclusion?

N

Mz

985.2

20

6

5.185.22

z

Alpha level: 1-tailed test

-3 -2 -1 0 1 2 3

+3.09 +2.32 +1.645

= .05

= .01

= .001

zcv scores

Z table

One-tailed:

α = .05

zcv = 1.65

Z-test stat = 2.99

p = .00138

Conclusion: Afr-Amer perform significantly different compared to Caucasian pop

Self-test problems (p200)

A researcher is interested in whether students who play chess have higher average SAT scores than students in the general population. A random sample of 75 students who play chess is tested and has a mean SAT score of 1070. The average for the population is 1000 (σ = 200).

Is this a one- or two-tailed test?

What are the null and alternative hypotheses?

Compute the z-test

What is zcv?

Should the null be rejected? What is the conclusion?

Self-test problems (p200)

1-tailed

H0: µchess = µpopulation ; Ha: µchess > µpopulation

Z =

Zcv = +/- 1.645

Reject null (H0). Students who play chess

score significantly higher on the SAT.

N

Mz

03.3

75

200

10001070

z

Errors

Type I

error

Correct

decision

Correct

decision

Type II

error

Actual situation

NO Effect Effect

H0 True H0 False

Reject H0

Retain H0

Experimenter’s

Decision

Conclude there was

an effect when there

actually wasn’t – the

risk of that is

Conclude there wasn’t

an effect when there

actually was an effect –

also called

Type I and Type II errors

Type I: Say significant diff when isn’t true Conclude treatment has an effect but really doesn’t

Type II: Miss a significant result Conclude no effect of treatment when it really does

Which is worse error to make?

Examples: Law:

Type I: Jury says guilty when innocent

Type II: Jury says innocent when guilty

Medicine: Type I: Doctor says cancer present when isn’t

Type II: Doctor says no cancer when it is there

Answer: it depends!

Setting your alpha level

Lower alpha (.05

to .01) to

minimize chance

of Type I error

But, then

increase chance

of Type II error!

Concerns with Alpha

All-or-none decision

Reject or accept null hypothesis

Alpha (criteria) is set arbitrarily

Null hypothesis logic is artificial

No such thing as “no effect”

Doesn’t give size of effect

p-value is chance of occurrence

Can not say “very significant”!

Sample size changes p-value

Statistical Power

What is the probability of making the correct decision??

If treatment effect exists either…

We correctly detect the effect or…

We fail to detect the effect (Type II error or )

So, the probability of correctly detecting is 1 -

Power: probability that test will correctly reject null

hypothesis (i.e. will detect effect)

Power depends on:

Size of effect

Alpha level

Sample size

-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3

Reject H0

Concerns with z-test

Make many assumptions!

Must know population mean and deviation

Must have a normal distribution

Must have a sample size where N < 30

If don’t know above info or can’t make

assumptions need to use other statistics!