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Statistics – Slides from the Podcast
(The text of the podcast narration begins on page 4 below)
Descriptive Statistics
Measurements of subject responses on a variable are summarized using descriptive statistics:
A
histogram
plots score ranges along the horizontal axis and score frequencies along the vertical
axis.
Basic Descriptive Measures
The
central tendency
is a statistic that indicates what the typical score is like in the distribution of
scores.
Mean
:
Statistical average of all scores.
Median
:
The fiftieth percentile (half of the scores are above this score, half are below).
Mode
: The most frequent score.
Basic Descriptive Measures (Cont.)
Relative standing:
Percentile rank
.
Variability is how dispersed the scores are relative to the average score.
Standard deviation
:
The average of how much the participant scores deviate from the mean.
The Normal Distribution
Examples: Height, Aggressiveness, IQ Test Scores, Anxiety
Features of the Normal Distribution
0
5
10
15
20
25
30
'60 '59 '58 '57 '56 '55 '54 '53 '52 '51 '50 '49 '48 '47 '46 '45 '44 '43 '42 '41 '40 '39 '38 '37 '36 '35 '34 '33 '32 '31 '30 '29 '28 '27 '26 '25 '24 '23
34.1%
34.1%
13.6%
13.6%
2.1%
0.1%
0.1%
3
Standard
Deviations
2
Standard
Deviations
1
Standard
Deviation
+1
Standard
Deviation
+3
Standard
Deviations
+2
Standard
Deviations
Mean
2.1%
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Approximating the Normal Curve
Very often a distribution can deviate from a perfect normal curve but yet be close enough that all
the statistics that assume a normal curve still work well.
For example, exam scores often approximate a normal curve.
Inferential Statistics
When differences between conditions are found, were they due to chance or to real differences
among the different conditions?
Mathematical tests of
statistical significance
answer this question.
pvalue
: Probability the result was due to chance.
By convention in psychology, when p = .05 or less, the result is taken to be significant.
Variance and Significance
Same mean, difference variance
Be Careful with Statistical Inferences
When a difference is significant, you can conclude that it is real. However, the fact that a difference
is statistically significant does NOT mean that it is large or important.
The difference may or may not be large or important.
Whether a significant difference is large or important will depend on other considerations.
Inference Example 1:
Suppose there was a product called the Genius Calculus Study Program that was priced at $5,000.
We decide to do an experiment to see if the program works.
We randomly assign one group of students to study for 10 hours a week with the Genius Calculus
Study Program, and another group of students to study 10 hours a week in their usual way.
Inference Example 1 Continued
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 Spring '08
 KOWLER
 Statistics, Normal Distribution, Standard Deviation, Mean

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