1. Introductory Psychology: Statistical Analysis
Ap psychology: Unit I
The use of mathematics to organize, summarize and interpret numerical data

2. Statistical Analysis: The Basics on Distributions
Part one

3. 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

4. Analysis: The Basics on Distributions
Glasses of H2O
# of People 1 2 3 4 5 6 7 8 9 10
Histogram
Polygon
Frequency Distribution

5. 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.

7. 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

8. The height of NBA players
The height of hobbits
The height of NBA players

9. Statistical Analysis: Descriptive Statistics
Descriptive statistics are used to organize and summarize data
Part two
Key Descriptive Statistics
Central Tendency
Variability
(Correlation Coefficient)

10. Analysis: Descriptive Statistics
WHY is the description of data important?

11. 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
Numbers that best represent the most typical score of a frequency distribution

12. Outliers IMPACT the mean! Outliers IMPACT the mean!
Ali
Ben
Carol
Sara
Evan
Greg
Hal
Inga
Jay
Mary 95 98
100
102
103
139
150
160
Outliers IMPACT the mean!
Mean IQ Score (114.6)
Median IQ Score (101)
Outliers IMPACT the mean!

13. 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

14. 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

16. Standard Deviation in Action

17. Standard Deviation in Action
68.3% of population
1SD

18. Standard Deviation in Action
95.4% of population
2 SD

20. 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?”

21. Analysis: Inferential Statistics
Statistical analysis of two (or more) sets of data to:
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

22. 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

23. 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?

24. Types of Correlation Negative Correlation Positive Correlation
The variables go in opposite directions.
Positive Correlation
The variables go in the SAME direction.
Studying and grades hopefully has a positive correlation.
Heroin use and grades probably has a negative correlation.