


Sherril M. Stone, Ph.D. 

Department of Family Medicine 

OSUCollege of Osteopathic Medicine 






IV Ð manipulated or controlled variable 

DV Ð condition/behavior of interest, measured 

Treatment Ð 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 






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 (H_{0}) Ð special handling does not
affect infant wgt 

ALTERNATIVE (H_{1})  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 2yr
olds? 

DIRECTIONAL Ð hypothesize increase in DV
(extra handling increases wgt) 

NONDIRECTIONAL Ð 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 





P Ð is not the probability that H_{0} is True 

P Ð is not the probability of a Type I error 

P Ð is not the probability of making a wrong 

decision 

P Ð is not the probability that sample statistic
is due to chance 

P Ð IS the probability of calculated data if H_{0} is True 






Test for ANY difference between means? 
Twotail 

Test < or > between means?  Onetail 

1. Rejection region  distribution above the
critical value 

2. Errors 

Type I 
rejecting true H_{0} 

Type II  accepting false H_{0} 

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 Ð tests relationship between
X and m 

results are descriptive of X to m 

3 possible alternative hypotheses (H_{1}) 

X =
m_{0} 

X <
m_{0} 

X >
m_{0} 



H_{0}: X = m_{0} 

H_{1}: X ¹ m_{0} Always assume H_{0} is true 



In Research Ð we want to reject H_{0} Ð
this indicates our X is different from m_{0} 






Significance level Ð setting the a 

a 
our choice of probability (p) value Ð (.05  .01  .001  etc.) 

.05 = 5 (out of 100) chances of being different 

.p < a  reject H_{0}, accept H_{1}
(this is statistically significant) 

.p > a  accept H_{0}, reject H_{1}
(this is NOT statistically significant) 

Rejection Region 

reject H_{0} = sample x is significantly
different than m 

Critical values Ð calculated test
values 

zscores (must know m and σ) 

tscores (when m and σ are not known Ð more common method) 

If sample zscores in tail Ð reject the H_{0}
(you found sig. diff) 

if sample zscores in body Ð accept the H_{0}
(you found NO sig.) 





EXAMPLE 1 



H_{0}: X
= 18 

H_{1}: X 18 

a = .05 

X =
15 

m = 18 

SD
= 1.6 

z
= X  m 

SE 




CohenÕs d = 

X  m_{0} 

_{
}s 





d = .20 Small 

d = .50 Medium 

d = .80 Large 

