Transcript UTOPPS—Fall 2004

UTOPPS—Fall 2004
Teaching Statistics in Psychology
AP Psychology “Suggestions”
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Descriptive Statistics
Measures of central tendency
 Variability
 Correlation
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Experimental Design
Appropriate Sampling
 Control
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Measures of Central Tendency
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Mean
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Median
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True average
True middle of sorted data
Mode
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Most frequent data value
How these measures relate
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In a normal distribution…
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Mean = Median = Mode
In a nonnormal distribution (one
that is skewed)…
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The mean will be impacted by the
unusual values and will be pulled
toward the skew.
Examples
Which measure do you use?
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If the distribution is close to
normal, they are all equal and it
makes no difference
If the distribution is skewed, the
median is the best measure of
center because it is “resistant” to
influence from outliers that
cause the distribution to be
skewed.
Variability
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Variation occurs
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there may be a center to the data, but each
individual value will vary around that center
Range of the data (max-min)
Quartiles (divide the data into quarters)
Interquartile Range (Q3 – Q1)
Standard Deviation
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Average distance that a data point lies away
from the mean
As a rough estimate—figure out the distance
that each data value lies from the mean, and
take the average
Not an exact calculation, but it gives a rough
idea.
Practicing Calculations
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1,1,2,3,4,5,6,7,8,9,10,16
Median (easiest)
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5.5 (average between 5 and 6)
Mean
Add ‘em all up and divide by 12
 6
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Mode
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1 (occurs most frequently)
More Practice
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1,1,2,3,4,5,6,7,8,9,10,16
Range
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Quartiles
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16 – 1 = 15
Medians of the lower and upper halves
Q1 = 2.5
Q3 = 8.5
Interquartile range
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Q3 – Q1 = 6
Standard Deviation
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1,1,2,3,4,5,6,7,8,9,10,16
The formula for standard deviation is
quite complicated, but we will use a
procedure to estimate this value.
The mean value is 6
The differences between each data
point and 6 are all follows:
-5, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 10
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Square those differences, add them
all up and divide by 12 and then
square root.
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(25+25+16+9+4+1+1+4+9+16+100)/12
Square root your answer
When to use Standard
Deviation
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Standard deviation (like the
mean) is impacted by unusual
values, so should not be used
unless the distribution is close to
normal.
If the distribution is normal,
standard deviations are an
excellent way to see how
variability within the data.
Empirical Rule
How to interpret and use
standard deviations
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More than three standard deviations
away from the mean is unusual, not
impossible
If you see a result like this, we
attribute that to mean that something
unusual is occurring
We sometimes use this as evidence
against the current mean
We sometimes use a p-value to
indicate how unusual this result is
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Something is considered unusual if the
p-value is small (p < .05). Look back at
the empirical rule slide…
Z-scores
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Measure the number of standard
deviations that a data point lies from
the mean
If z is negative, the data point is
below the mean
If z is positive, the data point is
above the mean
Z = (data point – mean) / st. dev
If z is more than 2.5, then it is
considered unusual in most settings
AP Psych Exam 2003
A. Statistics are often used to describe and
interpret the results of intelligence
testing.
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Describe the three measures of central
tendency
Describe a skewed distribution
Relate the three measures of central
tendency to a normal distribution
Relate the three measure of central
tendency to positively skewed distribution
• An intelligence test for which the scores
are normally distributed has a mean of 100
and a standard deviation of 15. Use this
info to describe how the scores are
distributed.
• In two normal distribution, the means are
100 for group I and 115 for group II. Can
an individual in group I have a higher
score than the mean score for group II.
Explain.
Correlation between two
quantitative variables
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Correlation is not Causation
Correlation shows that some linear
relationship exists.
Correlation Coefficient
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-1 < r < 1
-1 shows a very strong negative
relationship
1 shows a very strong positive
relationship
0 shows no correlation between the
variables
Correlation between
categorical variables
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Difficult to assess
Comparing percentages can be
misleading
Bar graphs can be misleading