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

The height of hobbits

The height of NBA players

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

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

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

Standard Deviation in Action

1SD 1SD

68.3% of population

Standard Deviation in Action

Standard Deviation in Action

2 SD 2 SD

95.4% of population

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