Transcript Evaluating Hypotheses

Testing
Hypotheses II
Lesson 10
A Directional Hypothesis (1-tailed)
Does reading to young children
increase IQ scores?
 m = 100, s = 15, n = 25
 sample mean also same
 zobs will be the same as 2-tailed test
 Differences from nondirectional
 hypotheses
 critical region ~

A Directional Hypothesis
1. State hypotheses
 H1: m > 100
Reading to young children will
increase IQ scores.


H0: m < 100
Reading
to young children will
decrease or not change IQ scores. ~
A Directional Hypothesis
2. Set criterion for rejecting H0
 a = .05, level of significance
 directional (one-tailed) test
 zCV = +1.645
critical
value for area = .05
in upper tail ~
Critical Regions
a = .05
zCV = + 1.645
f
-2
-1
0
+1
+2
+1.645
3. Collect sample & compute statistics
m  100, s  15
assume : X  105.5
sX 
zobs 
s
n
X m
sX
n = 25
15
3

25
105.5  100
5 .5


 1.83
3
3
Critical Regions
a = .05
zCV = + 1.645
f
-2
-1
0
+1
+2
+1.645
4. Interpret Results
Is zobs in the critical region?
 yes
 reject H0, accept H1
 These data suggest that reading to
young children does increase IQ.
 Difference is statistically significant
 but not for 2-tailed test
 lower criterion than 2-tailed ~

Significance of Result
If reject H0
 Statistical significance
 difference between groups is ...
greater than expected by chance alone
 Does NOT say it is meaningful
 Even very small effects can be
statistically significant
 How? ~

Significance of Result
If fail to reject H0
 Data are inconclusive
 Does not mean that there is no difference
 Why might there be a Type II error? ~

Practical Significance
Extent to which difference is important
 Magnitude of effect
 Independent of statistical significance
 Effect size
 APA recommends it be reported
 Pearson’s correlation coefficient, r

Will

cover later
Cohen’s d ~
Effect Size: Cohen’s d
Standardized measure
 Units of standard deviation
 General form

mean difference
d
standard deviation

For z test:
d
X m
s
Evaluating Effect Size:
Cohen’s d
For t-test:
X m
d
s

Cohen’s d

Small:
d = 0.2

Medium: d = 0.5

High:
d = 0.8
Significance Testing: Issues
Focus on H0 rather than data
 H0 is always false
 Small differences can be statistically
significant
 Focus on results of single study
rather than accumulation
 Focus on a, ignoring b
 Focus on p-values misleading
 Dichotomy vs continuum ~

Significance Testing: Alternatives
Criticized by some scientists
 As inappropriate
 Alternatives
 Confidence intervals
 Effect size
 Meta-analysis ~
