Transcript Statistics for the Behavioral Sciences (5th ed

Statistics for the Behavioral Sciences (5th ed.)
Gravetter & Wallnau
Chapter 8
Introduction to Hypothesis Testing
University of Guelph
Psychology 3320 — Dr. K. Hennig
Winter 2003 Term
The logic


experience->
question (What is it? Why…?)->
insight (hypothesis)->
“Is it so?”
As text has it:
Intelligence
Intelligability
• State your hypothesis (e.g., MIQ for voters is =110)

thus we would predict that our sample M = 110
• Obtain a random sample from the population (e.g., n =
200 registered voters) and compute M
• Compare M with predicted M
Fig. 8.2
Population
Sample
a) actual research situation
Tx
Treated
Sample
b) pt. of view of hypothesis test
Population
Tx
Treated
Sample
Step 1: State the hypothesis





Question: does handling a infant have an
effect on body weight?
null hypothesis stated: assume that in the
general population there is no change, no
effect, no difference (nothing happened)
H0: infants handled = 26 lbs. (even with
handling)
the alternative hypothesis states there is a
change, effect, difference
H1: infants handled <> 26 lbs. (handling makes
a difference) - both ref. to popultns
Step 2: Set the criteria


If the Ho is true, sample means will be close
to the null hypothesis
unlikely sample means will be very different
from the null hypothesis (in the tails of the
distribution)
• criteria separating the likely from the unlikely
sample


Alpha level ( or level of significance): p
value used to define the unlikely sample
critical regions: very unlikely if the null
hypothesis is true - if sample falls within,
reject null hypothesis
Set the criteria (contd.)


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
 = .05 (boundaries separate the extreme
5% from the middle 95%)
see Column C (the tail) in the tail: z =
1.96 and z = -1.96
Similarly,  = .01, 99%: z =  2.58
Similiary,  = .001: z =  3/30
Step 3: Collect data


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
Select parents and randomly assign to
training program of daily handling (= Tx)
Weigh after 2 years
summarize the data using the appropriate
statistics (e.g., M)
Compare with the null hypothesis by
transforming into z-score
z
M 
M
Step 4: Make a decision (“It is/not so!”)

Calculate: M = 30 lbs. at age 2; sample
size = n = 16, and  = 4
M
z

4
4


 1
n
16 4
M 
M
30  26 4

  4.00
1
1
(contd.)

Why do we focus on the null hypothesis?
Why assume there is no change?
• negative thinking?
• “innocent until proven guilty?” - burden of proof




“Is it so?” vs. “Is it not so?”
Logically, easier to falsify vs. verify (?)
E.g., All dogs have four legs!
E.g., state, the Tx works and then try and
prove vs. the Tx has no effect and try to
show false (conclude: insufficient evidence)