


Sherril M. Stone, Ph.D. 

Department of Family Medicine 

OSUCollege of Osteopathic Medicine 





tTest Ð hypothesis testing technique to reach
conclusion about m based on sample results 

z uses σ (pop SE) 

t uses s (sample SE) 







Table values Ð mathematically derived
theoretical distribution values 

Significance level Ð setting the a 

a is
probability (p) value Ð (.05, .01, .001)  .05 = 5 (out of 100) 

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

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

Rejection Region 

reject H_{0} if X significantly different from m (IV had affect) 

If df not in table Ð use next lower 

t _{.05} (14 df)_{obs} = 3.862 ³
t _{.}_{05} (14 df)_{tab} = 2.145 (reject H_{0}) 

t _{.05} (14 df)_{obs} = 1.789 ²
t .05_{ }(14 df)_{tab} = 2.145 (accept H_{0}) 







t
= X m_{0} 



SE 



Interpretation Ð always uses terms of experiment
and direction of difference 

Generalizability Ð is it random sample &
does it apply to similar samples? 

Uses of t 

Checking claims, norms, noerror standards, etc 

Simplest test for hypothesis testing 





EXAMPLE 1 

N = 16 

__ 

X = 181.62 



m_{0} = 180.19 



SD
= 1.6 



SE
= 1.6 

ÃN 

t
= 




4 6 8 

9 5 3 

7 5 2 

7 6 1 

6 6 9 

4 7 7 

2 8 6 

8 3 5 

7 4 

7 6 

4 7 




10 34 16 

19 16 17 

17 25 28 

17 35 33 

26 26 32 

14 16 21 

22 27 19 

28 28 27 

27 33 26 

27 24 15 





Example 1 

N =
38 

df = 381 = 37 

t =
5.3 

Calculate r^{2} 





Experimental method Ð mean of one group is
compared to mean of a different group after some type of treatment has been
applied to either group. 

Independent variable Ð manipulated variable 

Dependent variable Ð measured variable 

Treatment Ð the manipulation 

Experimental (treatment) group Ð the group
receiving the treatment 

Control group Ð the group not receiving
treatment 




Define H_{0} and H_{1} 

H_{0}: X = μ 

H_{1}: X ¹ μ 

Assume treatment has no effect (H_{0}) 

Choose a (.05 Behavioral/.01 or .001 Medical Sciences) 

Choose correct inferential statistic 

Calculate the statistics for your sample data 

Compare calculated results to the Table value 

Write interpretation using terms of experiment 







You must know the design before you analyze data 

IV and DV will not indicate the design 

Different ttests used for each design 

Independent Samples Ð no reason to pair the data 



Correlated Samples Ð matches the data 

Natural pairs 

Matched pairs (splitlitter for animals, twins,
siblings) 

Repeated measure 



If ttest is significant Ð then difference in
participant is due to the treatment 





There no reason to pair the data 

Randomly assign participants to groups 

One group receives treatment, other group does
not 

If ttest is significant Ð treatment had an
effect 





You are interested in the effects of an
antianxiety drug on weight loss. The drug group (7 rhesus monkeys)
received the drug while the control (placebo) group (6 rhesus monkeys) was
given a sugar pill (placebo). The monkeys were tested every Monday for 7
weeks. Their results served as the dependent variable. The H_{0}
was that the drug had no effect on weight. The H_{1} was that the
drug had an effect on weight. 







Natural pairs 

researcher does not pair 

naturally occurring pair 

pairing is based on logical, memberships, etc 

Matched pairs (splitlitter for animals, twins,
siblings) 

researcher controls the pairing 

may pretest to determine pair mate 

randomly assign each pair mate to treatment
& control 

Repeated measure 

pre and post test design 

each participant serves as own control 

If ttests are significant Ð then difference in
participants is due to the treatment 





You are interested in the effects of a new
diabetes drug for preteen
girls. You take a sample of blood from a group of 14 Caucasian
12year old girls then give them a dosage of the drug. The girls spend the day
together and eat the same meals. They monitor their insulin levels during
the day as usual. At the end of the day, you take another sample of blood.
The data consists of 14 pairs of pre and post insulin levels. The H_{0}
is that the new drug did not affect the insulin levels. The H_{1}
is that after the new drug, the girlsÕ insulin level will decrease. 




You are interested in the number of viral
infections that the average married couple experiences in a year. You ask
30 couples to participate in your study. You separate the spouses and ask
them how many colds they have in the past year. Your H_{0} was that
the gender does not make a difference in the number of colds reported. The
H_{1} was that the females experience more colds than the males. 





Stretching before running may decrease quad
strains thus reducing the need for medication. Athletes in the same
physical condition and with the same running time volunteered to
participate in the study. Group 1 did not stretch but Group 2 stretched.
Both groups ran 3 miles everyday for 2 weeks (14 days). The number of
muscle strains for each runner is presented. Determine if the groups
significantly differ Ð i.e. if stretching was effective in decreasing quad
strains and medication. 




The researcher in Example 4 decided to
replicate her results by conducting a second study. However, before the
run, 3 runners dropped out of the control group and 2 joined the
experimental group. The
researcher decided to conduct her study anyway. Determine if the groups
significantly differ Ð i.e. was stretching effective and reduced quad
strains and medication. 




Fatty food is hypothesized to correlate with
obesity. Your obese patients (all 75 lbs. overweight) are weighed before
beginning your study (preweight) and again after 1 year of not eating any
fatty food on a list you provide for them (all other lifestyle behaviors
remain the same). Your patients again are weighed at the end of the year.
Their pre and postweights are presented. Determine if the pre weight
significantly correlated to the post weight Ð i.e. does consumption of
fatty foods predict obesity. 

