Testing Hypotheses II Lesson 10

A Directional Hypothesis (1-tailed) n Does reading to young children increase IQ scores?  = 100,  = 15, n = 25 l sample mean also same l z obs will be the same as 2-tailed test n Differences from nondirectional l hypotheses l critical region ~

A Directional Hypothesis 1. State hypotheses H 1 :  > 100 u Reading to young children will increase IQ scores. H 0 :  < 100 u Reading to young children will decrease or not change IQ scores. ~

A Directional Hypothesis 2. Set criterion for rejecting H 0  =.05, level of significance l directional (one-tailed) test l z CV = u critical value for area =.05 u in upper tail ~

Critical Regions f  =.05 z CV =

3. Collect sample & compute statistics n = 25

Critical Regions f  =.05 z CV =

4. Interpret Results n Is z obs in the critical region? l yes l reject H 0, accept H 1 l These data suggest that reading to young children does increase IQ. n Difference is statistically significant l but not for 2-tailed test l lower criterion than 2-tailed ~

Significance of Result n If reject H 0 n Statistical significance l difference between groups is... greater than expected by chance alone n Does NOT say it is meaningful l Even very small effects can be statistically significant l How? ~

Significance of Result n If fail to reject H 0 l Data are inconclusive l Does not mean that there is no difference n Why might there be a Type II error? ~

Practical Significance n Extent to which difference is important l Magnitude of effect l Independent of statistical significance n Effect size l APA recommends it be reported l Pearson’s correlation coefficient, r u Will cover later l Cohen’s d ~

Effect Size: Cohen’s d n Standardized measure l Units of standard deviation n General form n For z test:

Evaluating Effect Size: Cohen’s d n Cohen’s d l Small: d = 0.2 l Medium: d = 0.5 l High: d = 0.8 For t-test:

Significance Testing: Issues n Focus on H 0 rather than data n H 0 is always false n Small differences can be statistically significant n Focus on results of single study rather than accumulation Focus on , ignoring  n Focus on p-values misleading n Dichotomy vs continuum ~

Significance Testing: Alternatives n Criticized by some scientists l As inappropriate n Alternatives l Confidence intervals l Effect size l Meta-analysis ~