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 H 1: µ ≠ 0
One-tailed test Directional hypothesis Predict increase or decrease H 0: µ = 0 H1: µ < 0 OR µ > 0
Which do you choose? What alpha do you choose?
Alpha level: 2-tailed test
= .05 = .01 = .001
-3
zcv scores -3.30 -2.58
-2
-1.96
-1
0
1
2
3
+1.96 +2.58 +3.30
Alpha level: 1-tailed test
= .05 = .01 = .001
-3
zcv scores
-2
-1
0
1
2
3
+1.645 +2.32 +3.09
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 18.50
Af-Amer 22.45
Asian 19.67
Latino 21.55
Inferential statistic: z-test z
(x X )
X
Z-score: 0.03
0.02
Density
Comparison of score with population distribution in terms of SD from population mean
0.01
Sampling distribution’s
Z-test: Comparison of sample mean with sampling distribution
50
100
150
IQ IQ for 1 Subject 80 70 60
Frequency
µx = µ σx < σ Standard error of mean = σx= σ/√N
0.00
50 40 30 20 10 0 85
95
105
115
Mean IQ for 10 Subjects
z
M
N
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?
z
M
N 22.5 18.5 z 2.985 6 20
Alpha level: 1-tailed test
= .05 = .01 = .001
-3
zcv scores
-2
-1
0
1
2
3
+1.645 +2.32 +3.09
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?
Zcv = +/- 1.645 Reject null (H0). Students who play chess score significantly higher on the SAT.
Errors Conclude there was an effect when there actually wasn’t – the risk of that is Reject H0
Experimenter’s Decision Retain H0
Actual situation NO Effect
Effect
H0 True
H0 False
Type I error
Correct decision
Correct decision
Type II error 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
Reject H0
-3
-2
-1
0-3
1-2
2-1
30
1
2
3
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!
