Download Statistics

CHS AP Psychology
Unit 1: Science of
Psychology
• Essential Task 1-8: Apply basic statistical
concepts to explain research findings:
- Descriptive Statistics: Central Tendency (mean,
median, mode, skewed distributions) Variance (
range, standard deviation, and normal
distributions) – Inferential Statistics: Statistical
significance (t-test and p-value)
Statistical Reasoning
Statistical procedures analyze and interpret data
and let us see what the unaided eye misses.
Composition of ethnicity in urban locales
Central Tendency
• Tendency of scores to
congregate around some
middle variable
• A measure of central tendency
identifies what is average or
typical in a data set
Measures of Central Tendency
Mode: The most frequently occurring
score in a distribution.
Mean: The arithmetic average of scores
in a distribution obtained by adding
the scores and then dividing by their
number.
Median: The middle score in a rankordered distribution.
But the mean doesn‘t work in a
skewed distribution…
The median is a much better
measure of the center
Skewed distributions
Look for the “tail of the whale”
Negatively Skewed
zero
• If the tail is
closest to
ZERO, it is
negatively
skewed.
• If it is far away
from ZERO, it
is positively
skewed.
Positively Skewed
zero
Measures of Variation
• Statistical dispersion (how
distributed the data points are)
is a key concept in statistics.
• Two key ways of measuring
statistical dispersion
 Range
 Standard Deviation
Range
The range simply gives the lowest and
highest values of a data set.
Let’s Roll the Dice!
• Get into pairs, and one person gets out a
piece of paper and writing utensil and the
other gets the 2 dice
• Writing utensil partner will create this chart:
Score Frequency
2
3
4
5
6
7
8
9
10
11
12
frequency
score
The best way to show this
data is to use a bar graph
Standard Deviation
•Standard deviation gives a
measure of dispersion.
– Essentially, they are measures of
the average difference
between the values.
•Standard deviation gives a value
that is directly comparable to
your mean values.
Standard Deviation in Action
• A couple
needs to be
within one
standard
deviation of
each other in
intelligence
(10 points in
either
direction). —
Neil Clark Warren,
founder of
eHarmony.com
Formulas for Standard Deviation
You will NOT need to know this for
the test. This is just to show you
how it is formulated to use in
statistical research
Normal Distributions
•The distribution of data also gives
us key info.
•We know that many human attributes…
e.g height, weight, task skill, reaction time,
anxiousness, personality characteristics,
attitudes etc.
•…follow a normal distribution.
Normal Distribution
IQ follows a Normal Distribution
You NEED to memorize this! We’ll touch on
it again in the Individual Differences Unit!
Mean = 100
SD = 15
What percentage score below
100?
Mean = 100
SD = 15
2.1%
13.6%
34.1%
What percentage score above
100?
Mean = 100
SD = 15
34.1%
+ 13.6% + 2.1%
Statistical Significance
• How two groups’ means are different
– If graphed data does not overlap or
overlaps a bit, difference IS SIGNIFICANT
• Significance allows you to say how likely the
difference in the means is due to CHANCE
– Goal is .05 difference, or 5% due to
chance, which isn’t a lot
•If it end up .75 difference, the more
chance affected the outcome.
– The larger the number, the more likely
chance had to do with the difference in
the outcomes.
Normal Distribution
What percentage score between
85 and 100?
34.1%
Mean = 100
SD = 15
Normal Distribution
What percentage score between
85 and 115?
Mean = 100
SD = 15
34.1%
+ 34.1%
= 68.2%
What percentage score between
70 and 130?
Mean = 100
SD = 15
13.6%
+
34.1%
+ 34.1%
+ 13.6%
= 95.4%
What percentage score below 70
and above 130?
Mean = 100
SD = 15