Transcript Statistics –AP psych review

Statistics
Lecture of 9-8-08
Frequency distribution stats (arranges
ALL of the scores received):
• Histograms –frequency distributions of
continuous data
• Bar graphs –used for discrete data (like if I
was comparing the GPAs of each class at
SW.)
• Frequency polygons –line graphs made by
connecting the tops of bars and erasing the
bars…
Scatter plots or scatter grams
• These are used to show a relationship or
correlation.
• Make one score the ‘X’ value on a graph
• Make the second score the ‘Y’ value on a
graph.
• Positive correlations have a positive slope
• Negative correlations have a negative slope
• Randomness implies no correlation
Test yourself, What is the following
graph saying?
The Beta test
and the SAT
test are similar.
People that
score well on
Beta also score
well on SAT.
Positive
correlation!
Test yourself, What is the following
graph saying?
The higher
the
temperature,
the lower
the
dissolved
oxygen in
the river.
Dissolved
Oxygen
level in a
river
Temperature in Celsius
What is this graph saying?
Heart rate doesn’t seem to change even though the length of
time it is measured changes.
What is this graph saying?
Not much. No correlation
Histogram or frequency polygon?
histogram
Histogram or bar graph?
Bar Graph
Histogram or frequency polygon?
Frequency polygon
Histogram or frequency polygon?
Both!
Central Tendency –statistics to
find the middle o’ the bunch!
• Mode: most frequently occurring score. This is the
LEAST used in statistics… just gives a quick look at
the data.
– 2 scores appear equally the most? ‘Bimodal’
– More than 2 appear the most? ‘Multimodal!’
• Median: middle score when the data is organized by
size.
• Mean: the mathematical average of a set of data.
(Most preferred method of finding central tendency)
Test yourself!
Given the set: 5,6,7,7,7,8,8,9,9,10
Mode? 7
Median? 7.5
Mean? 7.6
Distributions
• Normal distributions are where the data points
are in a symmetrical ‘bell shaped’ curve. This
occurs when the mode, median and mean are all
the same.
• Skewed distributions are when most of the
data points are squeezed into one end of the
curve.
– When the mean is lower than the median, it is a
negative distribution.
– When the mean is higher than the median, it is a
positive distribution.
Test yourself: Skewed or normal,
if skewed, positive or negative?
Test yourself: Skewed or normal,
if skewed, positive or negative?
Test yourself: Skewed or normal,
if skewed, positive or negative?
Variability
• A measure of the distribution of scores
• 3 types:
– Range (The highest score – lowest score)
– Variance (A measure of how different a score is
from the mean.)
– Standard Deviation (Another measure of how
different a score is from the mean.)
Facts about Variance and
standard deviation:
• Standard deviation scores fall between zero
and ½ the range.
• The closer a standard deviation is to zero,
the closer all scores fall near the mean.
• The higher the number is, the more varied
the scores.
More variability or less variability?
High Standard Deviation or Low?
Low standard deviation because scores center narrowly
around the mean.
Scores are pretty close to the mean, and the distribution is not very
wide, so there is less variability.
Confounding Variables –When you can’t
tell which variable is causing a change (in
the dependant variable…)
What are the confounding variables? A soccer coach wanted to
improve the team's playing ability, so he had them run two miles a day.
At the same time the players decided to take vitamins. In two weeks the
team was playing noticeably better, but the coach and players did not
know whether it was from the running or the vitamins.
Here is another one: Ice cream consumption and murder rates are
highly correlated. Now, does ice cream incite murder or does murder
increase the demand for ice cream? Name some confounding variables.
How to prevent the confounds?
• Control as many variables as you can.
• Use a ‘double-blind’ experiment… one
where the experimenter doesn’t know who
has the treatment and who has the
placebo…