ap psychology: unit i introductory psychology: statistical analysis the use of mathematics to...
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AP PSYCHOLOGY: UNIT I
Introductory Psychology: Statistical Analysis
The use of mathematics to organize, summarize and interpret numerical data
PART ONE
Statistical Analysis: The Basics on Distributions
Analysis: The Basics on Distributions
Frequency Distribution A table or graph that shows how often different
numbers or scores appear in a particular set of scores
Histogram A bar graph that shows a frequency distribution
Polygon A line graph that shows a frequency distribution
Analysis: The Basics on Distributions
Glasses of H2O
# of People
1 0
2 1
3 2
4 4
5 5
6 6
7 5
8 4
9 2
10 11 2 3 4 5 6 7 8 910
01234567
Glasses of Water
1 2 3 4 5 6 7 8 9 1001234567
Glasses of Water
Frequency Distribution
Histogram
Polygon
Analysis: The Basics on Distributions
The Normal (Bell) Curve A special frequency polygon in which the scores
are symmetrically distributed around the mean
Mean, median and mode
Used as a guideline for intelligence, height, weight,
etc.
Analysis: The Basics on Distributions
Positively Skewed Distribution Scores are concentrated at the low end of the
distribution
Negatively Skewed Distribution Scores are concentrated at the high end of the
distribution
Bimodal Distribution Frequency distribution in which there are two
high points rather than one
PART TWO
Statistical Analysis: Descriptive Statistics
Descriptive statistics are used
to organize and summarize data
Key Descriptive Statistics1.Central Tendency 2.Variability 3.(Correlation
Coefficient)
Analysis: Descriptive Statistics
Measures of Central Tendency Mean
The arithmetic average of ALL scores in a distribution
(Impacted by outliers) Median
The middle score in an ordered distribution of scores; the 50th percentile
(Not impacted by outliers) Mode
The most frequent score in a distribution of scores (Not impacted by outliers)
Numbers that best represent
the most typical score of
a frequency distribution
Ali Ben Carol
Sara Evan Greg Hal Inga Jay Mary
95 98 100 100 100 102 103 139 150 160
Outliers IMPACT the mean!
Mean IQ Score (114.6)Median IQ Score (101)
Outliers IMPACT the mean!
Analysis: Descriptive Statistics
Measures of Variability Range
The difference between the highest &lowest scores in a distribution
Standard Deviation The measure of the average
difference between each of the values in a data set
If the scores are clustered around a central point, the measures of variability
will be SMALLER…
Refers to how much the
scores in a data set vary
from each other and from
the mean
Scores are clustered around a
central point; smaller range and standard
deviation
Scores are more spread out and NOT clustered around
a central point; larger range and standard
deviation
PART THREE
Statistical Analysis: Inferential Statistics
“Is there a difference between the means of the two samples?”
“Are these results statistically significant?”
If we have results from two (or more) samples, we can ask…
Analysis: Inferential Statistics
Inferential Statistics Statistical analysis of two (or more) sets of data
to: 1. Reduce the possibility of error in measurement2. Determine if the differences between the data sets
are greater than chance variation would predict
Inferential statistics look for statistical significance
A statistical statement of how likely it is that an obtained result occurred by chance A t-test is used to determine whether two means
are significantly different; yields a p-value
Analysis: Inferential Statistics
p-value A measure of confidence in the observed
difference
Allows researchers to determine the probability that the difference was due to chance A p-value of LESS than 0.05 (<o.05) is the common
criterion for statistical significance Translation
The probability that the results are due to chance alone is less than 5 times out of 100
One can be 95% certain that the results are real and not due to chance alone