Chapter 3
Normal Curve, Probability, and
Population Versus Sample
Part 2
Using the Table: From % back to
Z or raw scores
• Steps for figuring Z scores and raw scores
from percentages:
1. Draw normal curve, shade in approximate
area for the % (using the 50%-34%-14% rule)
2. Make rough estimate of the Z score
where the shaded area starts
3. Find the exact Z score using the normal
curve table:
– look up the % and find its z score (see example)
(cont.)
4. Check that your Z score is similar to
the rough estimate from Step 2
5. If you want to find a raw score, change
it from the Z score, using formula:
x = Z(SDx) + Mx
Probability
• Probability
– Expected relative frequency of a particular
outcome
• Outcome
– The result of an experiment
Possible successful outcomes
Probabilit y 
All possible outcomes
Probability
• Range of probabilities
– Proportion: from 0 to 1
– Percentages: from 0% to 100%
• Probabilities as symbols
–p
– p < .05 (probability is less than .05)
• Probability and the normal distribution
– Normal distribution as a probability distribution
– Probability of scoring betw M and +1 SD = .34
(In ND, 34% of scores fall here)
Sample and Population
• Review difference betw sample & pop
• Methods of sampling
– Random selection – everyone in the pop has
equal chance of being selected in sample
– Haphazard selection (e.g., convenience
sample) – take whomever is available,
efficient  may differ from pop.
Sample and Population
• Population parameters and sample statistics–
note the different notation depending on whether
we refer to pop or sample
– M for sample is  for population
– SD for sample is  for population
Ch 4 – Intro to Hypothesis
Testing
Part 1
Hypothesis Testing
• Procedure for deciding whether the
outcome of a study (results for a sample)
support a particular theory (thought to
apply to a population)
• Logic:
– Considers the probability that the result of a
study could have come about if the
experimental procedure had no effect
– If this probability is low, scenario of no effect is
rejected and the theory is supported
The Hypothesis Testing Process
1. Restate the question as a research hypothesis
& a null hypothesis
• Research hypothesis –supports your theory.


Job satisfaction of Dr. Johnson is higher than national
average (M = 3.5 on 1-5 scale)
Null hypothesis – opposite of research hyp; no
effect (no group differences). This is tested.

Job satisfaction of Dr. J does not differ from national
average
The Hypothesis Testing Process
2. Determine the characteristics of the
comparison distribution


Comparison distribution – what the
distribution will look like if the null hyp is
true.
If null is true, Dr. J’s score = National M
(which was 3.5).
Note – given sampling errors, we know that
the Dr. J is likely to differ from 3.5 at least
a little…so…
The Hypothesis Testing Process
3. Determine the cutoff sample score on the
comparison distribution at which the null
hypothesis should be rejected



Cutoff sample score (critical value) – how
extreme a difference do we need (betw Dr. J
& nat’l M) to reject the null hyp?
Conventional levels of significance:
p < .05, p < .01
We reject the null if probability of
getting a result that extreme is .05 (or .01…)
Step 3 (cont.)
 How do we find this critical value?
 Use conventional levels of significance:
p < .05, p < .01
 Find the z score from Appendix Table 1 if 5% in tail
of distribution (or 1%)
For 5%  z = 1.64
 We reject the null if probability of getting a result that
extreme is .05 (or .01…)
 Reject the null hyp if my sample z > 1.64
 Means there is only a 5% (or 1%) chance of getting results
that extreme if Null is true, so we’d reject the null if we’re in
the rejection region (z > 1.64)
The Hypothesis Testing Process
4. Determine your person’s score on the
comparison distribution


Collect data, calculate the z score for your person of
interest
Use comparison distribution – how extreme is that
score?
5. Decide whether to reject the null hypothesis



If your z score of interest falls within critical/rejection
region  Reject Null. (If not, fail to reject the null)
Rejecting null hypothesis means there is support for
research hypothesis.
Example?