Download Chapter 3 part 2 / Chapter 4 part 1

Chapter 3
Normal Curve, Probability, and
Population Versus Sample
Part 2
Tues. Sept. 3, 2013
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
• 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
• Population parameters and sample statistics–
note the different notation for 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
support a particular theory
• 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.


Example?
Null hypothesis – opposite of research hyp; no effect
(no group differences). This is tested.

Example?
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.
 Example?
Note – we recognize there will be sampling errors in our
sample mean
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 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
 What does it mean to reject the null at .05 alpha level?
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?