Transcript Statistics PPT

Introductory Psychology:
Statistical Analysis
AP PSYCHOLOGY: UNIT I
The use of mathematics to
organize, summarize and
interpret numerical data
Statistical Analysis:
The Basics on Distributions
PART ONE
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
1
Frequency Distribution
Glasses of Water
Histogram
Glasses of Water
7
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Polygon
1 2 3 4 5 6 7 8 9 10
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
The height
of hobbits
The height
of NBA
players
Statistical Analysis:
Descriptive Statistics
Descriptive statistics
are used to organize
and summarize data
PART TWO
Key Descriptive Statistics
1. Central Tendency
2. Variability
3. (Correlation Coefficient)
Analysis: Descriptive Statistics
WHY is the description of data important?
Analysis: Descriptive Statistics
 Measures of Central Tendency
 Mean
The arithmetic average of ALL
scores in a distribution
 (Impacted by outliers)


Median
Numbers that
best represent
the most typical
score of a
frequency
distribution
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)

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

Refers to how
much the scores
in a data set
vary from each
other and from
the mean
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…)
Scores are more spread out
and NOT clustered around a
central point; larger range
and standard deviation
Scores are
clustered around
a central point;
smaller range
and standard
deviation
Standard Deviation in Action
Standard Deviation in Action
68.3% of population
1SD
1SD
Standard Deviation in Action
95.4% of population
2 SD
2 SD
Statistical Analysis:
Inferential Statistics
PART THREE
If we have results from two (or more) samples, we can ask…
“Is there a difference between the means of the two samples?”
“Are these results statistically significant?”
Analysis: Inferential Statistics
 Inferential Statistics
 Statistical analysis of two (or more) sets of data to:
1.
2.

Reduce the possibility of error in measurement
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

Correlational Method
 Correlation expresses a
relationship between
two variables.
 Does not show
causation.
As more ice cream is eaten,
more people are murdered.
Does ice cream cause murder, or murder cause people to eat ice cream?
Types of Correlation
Positive Correlation
 The variables go in the
SAME direction.
Negative Correlation
 The variables go in
opposite directions.
Studying and
grades hopefully
has a positive
correlation.
Heroin use and
grades probably has
a negative
correlation.