Download Stats HW

Name_______________________________
AP PSYCH
AIM: We will not fear statistics!
There are different ways that psychologists can show data and describe it for the specific group studied.
This is known as descriptive statistics.
A. One way to describe data is to show someone as being in a certain percentile. If a person is in the
74th percentile, this means 74% of students performed lower. Describe the percentiles of the
following students.
a. Mary
i. 20th percentile Math_____________________________
ii. 58th percentile English____________________________
iii. Which subject can we infer that Mary is better in?____________ Why?
b. Joe
i. 85th percentile Math_____________________________
ii. 45th percentile English___________________________
iii. Which subject can we infer that Joe is better in? ____________ Why?
*There is NO 100th percentile.
B. MEASURES OF CENTRAL TENDANCY (a single number that represents a whole set of scores)
a. 3 Ms
i. MEAN
ii. MEDIAN
iii. MODE
C. Skewed distributions
a. The MEAN is the __________________________________; however, it is the MOST
_______________________ to outliers or extreme scores.
In a normal distribution, the measures of central tendency tend to fall in the middle
0.004
Height of Curve
0.003
0.002
0.001
0
0
200
400
SAT Scores
600
800
b. In a POSITIVE or RIGHT SKEW… the MEAN is pulled
________________ because the outliers or extreme scores are on the
upper data points of x-axis. Yet, the bulk of the scores are on the
lower data points of x-axis. If this were test data, we could
conclude that, the majority did ________ , and a few outliers
_______________________________________
c. In a NEGATIVE or LEFT SKEW… the MEAN is pulled
________________ because the outliers or extreme scores are on the
lower data points of x-axis. Yet, the bulk of the scores are on the
upper data points of x-axis. If this were test data, we could
conclude that, the majority did ________ and a few outliers
_________________________
**MEMORY TIP! The “tail” of the skewed distribution graph points to the type of skew (tail pointing the
left=negative skew; tail pointing to the right=positive skew). This will help you remember what happens
to the mean in skewed distributions… Typically, in these cases, the MEDIAN is more accurate reflection of
group than the mean.
D. Dispersion or spread of scores (define)
a. Range
b. Variance
c. Standard Deviation
Using the bell curve provided...
1. Examine the Weschler Adult Intelligence (top) scale scores. What is the standard deviation?_______ points
2. Examine the SAT Math scale scores (below). What is the standard deviation?________ points
3. Which has a higher standard deviation: SAT or IQ test? What does this mean?
4. If your SCORE is 800 on the SAT Math Scale, how many standard deviations (z-scores) are you from the
mean?___________
5. What is the SCORE one standard deviation above the mean on the Wechsler Adult Intelligence
Scale?__________
the Z score is:_________
6. What is the SCORE one standard deviation below the mean on the SAT Math Scale? _____ The Z score is:___
E. The Empirical Rule or “68-95-99 Rule”
Pretend the mean is a 75% on an AP test. The standard deviation is 5. Draw what the curve might look like.
Draw at least two standard deviations away from the mean.
What does a Z score of +1 equal?_________ What about -2__________? (tells us how far away score is from
the mean)
What does that say about the scores of 68% of the class? They scored between _____ and _______. What
about 95% of class? They scored between ______ and _______
What % of class scores were above 85%?_________
II. Inferential statistics: The researcher can INFER about the
POPULATION based on what is known about the sample.
Statistic is a measure for a sample (n).
Parameter is a measure for the population (N).
Is the data for sample (n) descriptive of the population
(N)? We will never know, but we make an inference.
The larger the sample, the more representative, the
more reliable.


F. Statistical significance
 The results were not due to CHANCE
If p is LOW, .05 or .04 or .03 or .02 or .01
WE CAN REJECT NULL! The null hypothesis is what the researcher tries to disprove, reject,
or nullify. **You can never 100% fully prove anything in science; you can only reject the
null hypothesis, which is the opposite of the hypothesis (you can only disprove, not prove).
You can’t prove anything is 100% true because you can never know if it was 100% not due
to chance (never a 0% p-value) BUT if the p-value is less that .05%, you can be confident
enough (statistically significant)
NULL: (H0) A new vaccine does not change the proportion of people with a fever
ALTERNATIVE: (H1) A new vaccine has a LOWER proportion of people with a fever
p value = .0139
-What can we conclude?
H0: The new treatment does not improve mental health
H1: The new treatment does improve mental health
p value = .06
What can we conclude?
1. Basketball team data is as follows – calculate the measures of central tendency and draw a
frequency histogram. Does it have a positive or negative SKEW?
Jake
Scott
Josh
Bobby
Christian
Grant
Billy
Thomas
14 points
4 points
22 points
6 points
19 points
8 points
3 points
6 points
2. Two classes took the same psychology test. The scores for the first period class were: 81, 85, 94,
88, 80, 77, and 90. The scores for the second period class were: 55, 105, 92, 73, 95, 95, and 80.
Which group has the greater standard deviation? (I do not expect you to do any calculations)
3. IQ (intelligence quotient) scores are normally distributed with a mean of 100 and a standard
deviation of 16. What percentage of people have scores above 116?
4. What statistical technique would be appropriate for a researchers to use in trying to determine how
consistent intelligent scores are over time?
a. coefficient; b. mean; c. median; d. range; e. standard deviation
5. When a distribution of scores is skewed, the best representation of the central tendency is the:
a. Standard deviation; b. mean; c. median; d. coefficient
6. Which is NOT ethical? (Use your book—we will cover this last part on Monday)
a. Researchers must protect participants from needless harm and discomfort
b. Participants must take part in the study on a voluntary basis
c. Personal information about participants must be kept private
d. The research must be fully explained to participants when the study is completed
e. It is NEVER acceptable for a researcher to deceive a participant during research