Download 04. STATS.2016

THE ROLE OF
STATISTICS IN
RESEARCH
Reading
APPENDIX A: Statistics
pp. 673-677
Definition
A field of mathematics dealing with the analysis,
interpretation, and presentation of masses of numerical data
(Merriam-Webster’s Collegiate Dictionary).
There are three kind of lies: “Lies, damned lies, and statistics.”
Types of Statistics
Descriptive Statistics
- simple quantitative summaries of the data
- describe the basic features of the data in a study
Inferential Statistics
- used for testing hypotheses.
- complex calculations based on probabilities
- help reach conclusions about the data.
eg did these 2 samples come from the same population ?
We’ll focus on
Descriptive Statistics
Frequency Distributions
•
A summary of the frequency of individual scores on
one variable
•
i.e., How many people got each score
•
Nominal (categories) vs. Score (ordered) variables
•
Smooth curve vs. histogram
Histogram of of Psych 100 grades
Three Aspects of Distributions
1. SHAPE: flat, normal, skewed etc
2. CENTRAL TENDENCY: where is the "center" of a
distribution?
- Mean, median, or mode
3. VARIABILITY: how different are the scores from
each other?
1. Shapes of Distributions
The normal distribution
(bell-curve)
Flat distribution
More Shapes
Skewed distributions
Leans to right
Leans to left
2. Measures of
Central Tendency
MEAN
- average of the scores
- (Sum of scores)/Number of people
MEDIAN
- the middle score when ordered
MODE
- most frequent score
Shape is important too
Multi-modal distributions
0
2
They sometimes disagree
Mo
50, 60, 60, 99, 100 (Mean = 74)
Jo
50, 60, 70, 70, 90 (Mean = 68)
Flo
50, 50, 75, 76, 77 (Mean = 66)
2. Measures of Variability
RANGE:
- the highest value minus the lowest value
STANDARD DEVIATION:
- the average difference among the scores
e.g. of Variability
Two normal distributions
-same mean
--differ in variability
Normal Curve
Mean
3%
68%
13%
130
150
170
3%
13%
190
210
Standard Normal Curve
(in terms of standard deviations)
Mean
68%
-2
-1
0
+1
+2
Measuring associations
between variables:
The main goal of science
Plotting Associations
CORRELATION COEFFICIENT (r)
-quantifies associations
-plug your numbers into the
correlation formula (see book)
-yields a number between -1 and +1
Perfect positive correlation
Perfect Positive Correlation
10
8
6
Y
r = + 1.00
4
2
0
0
2
4
6
X
8
10
Perfect negative
Perfect Negative Correlation
10
8
r = - 1.00
6
Y
4
2
0
0
2
4
6
X
8
10
Strong Positive Correlation
10
8
6
Y
r = + .85
4
2
0
0
2
4
6
X
8
10
Zero correlation
Little or No Correlation
10
8
6
Y
4
r=0
2
0
0
2
4
6
X
8
10
SUMMARY
One variable:
• Frequency distributions
• measures of central tendency
• measures of variability
Two variables:
• correlations