Notes

Outline

Statistics 6 Hypothesis Testing Sherril M. Stone, Ph.D. Department of Family Medicine OSU-College of Osteopathic Medicine

Hypothesis Testing IV – manipulated or controlled variable DV – condition/behavior of interest, measured Treatment – the application of the IV Hypothesis testing - use sample data to make inferences about the population State a hypothesis about a population Use hypothesis to predict sample characteristics Obtain a random sample from the population Compare the sample data with the hypothesis

Example 1. State the hypothesis - early stimulation & mild stress result in increase infant  development (eyes open sooner, more rapid brain development, and faster growth) Avg wgt of 2 yr olds in population μ = 26 lbs NULL (H0) – special handling does not affect infant wgt ALTERNATIVE (H1) - infants who do not get special handling weigh less than 26 lbs 2. Use hypothesis to predict sample characteristics What do you predict as the wgt of the 2-yr olds? DIRECTIONAL – hypothesize increase in DV (extra handling increases wgt) NONDIRECTIONAL – no direction in DV (extra handling changes wgt) 3. Collect random sample data - randomly select sample of infants and train parents to provide extra daily handling (do not bias sample with all fat or skinny infants) 4. Compare sample data with predictions - compare  X  to μ

Errors

Probability P – is not the probability that H0  is True P – is not the probability of a Type I error P – is not the probability of making a wrong       decision P – is not the probability that sample statistic is due to chance P – IS the probability of calculated data if H0  is True

Bell Curve – Which Test to Use? Test for ANY difference between means? - Two-tail Test < or > between means? - One-tail 1. Rejection region - distribution above the critical value 2. Errors Type I -  rejecting true H0 Type II - accepting false H0 3. Level of significance (α) - probability of making Type I 4. Power of statistical test (1 - β) - probability of making           the correct decision to reject false null

Hypothesis Testing Using Z-Scores Hypothesis testing – tests relationship between X and m results are descriptive of X to m 3 possible alternative hypotheses (H1) X =  m0 X <  m0 X >  m0 H0:     X = m0 H1:     X ¹ m0 Always assume H0 is true In Research – we want to reject H0 – this indicates our          X  is different from m0

Hypothesis Testing Using Z-Scores Significance level – setting the a a - our choice of probability (p) value – (.05 - .01 - .001 - etc.) .05 = 5 (out of 100) chances of being different .p < a  -  reject H0, accept H1 (this is statistically significant) .p > a  -  accept H0, reject H1 (this is NOT statistically significant) Rejection Region reject H0 = sample x is significantly different than m Critical values – calculated test values z-scores (must know m and σ) t-scores (when m and σ are not known – more common method) If sample z-scores in tail – reject the H0 (you found sig. diff) if sample z-scores in body – accept the H0 (you found NO sig.)

Critical region boundaries for Z-scores

Z-score Hypothesis Testing Examples EXAMPLE 1 H0:   X  =  18 H1:   X     ≠  18 a   =   .05 X =  15 m     =  18 SD  = 1.6 z   =    X -  m             SE

Effect Size Index       Cohen’s d  =                            X  -   m0                                                s d = .20  Small d = .50 Medium d = .80 Large

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