Testing Hypotheses II

Lesson 10

A Directional Hypothesis (1-tailed)

Does reading to young children increase IQ scores?

= 100, = 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: > 100

Reading to young children will increase IQ scores.

H0: < 100 Reading to young children will

decrease or not change IQ scores. ~

A Directional Hypothesis

2. Set criterion for rejecting H0

= .05, level of significance directional (one-tailed) test zCV = +1.645

critical value for area = .05 in upper tail ~

Critical Regions

f

+1 +20-1-2+1.645

= .05

zCV = + 1.645

3. Collect sample & compute statistics

Xobs

Xz

105.5 :assume X

15100 ,n = 25

nX

25

15 3

31005.105

83.135.5

Critical Regions

f

+1 +20-1-2+1.645

= .05

zCV = + 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

For z test:

deviation standarddifferencemean

d

Xd

Evaluating Effect Size: Cohen’s d

Cohen’s d

Small: d = 0.2

Medium: d = 0.5

High: d = 0.8

For t-test:

sXd

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 , ignoring Focus on p-values misleading Dichotomy vs continuum ~

Significance Testing: Alternatives

Criticized by some scientists As inappropriate

Alternatives Confidence intervals Effect size Meta-analysis ~