Statistics
Descriptive Statistics
• Organize & summarize data (ex: central tendency & variability
Scales of Measurement
Nominal• Categories for
classifying• Least informative scaleEX: divide class based on
eye color
Ordinal• Order of relative
position of items according to some criterion
• Tells order but nothing about distance between items
Ex: Horse race
Scales of Measurement
Interval • Scale with equal
distance btw pts but w/o a true zero
• Ex: Thermometer
Ratio• Scale with equal
distances btw the points w/ a true zero
• Ex: measuring snowfall
Frequency Distribution
Histogram & Frequency Polygon
• X axis- possible scores• Y axis- frequency
Normal Curve of Distribution
• Bell-shaped curve• Absolutely symmetrical• Central Tendency:
mode, mean, median?
Central Tendency• Mean, Median and Mode.• Watch out for extreme scores or outliers.
$25,000-Pam $25,000- Kevin$25,000- Angela$100,000- Andy$100,000- Dwight$200,000- Jim$300,000- Michael
Let’s look at the salaries of the employees at Dunder Mifflen Paper in Scranton:
The median salary looks good at $100,000.The mean salary also looks good at about $110,000.But the mode salary is only $25,000.Maybe not the best place to work.Then again living in Scranton is kind of cheap.
Skewed Distributions
Positively Skewed Negatively Skewed
Bimodal Distribution
• Each hump indicates a mode; the mean and the median may be the same.
• Ex: Survey of salaries- Might find most people checked the box for both $25,000-$35,000 AND $50,000-$60,000
Variability
• On a range of scores how much do the scores tend to vary or depart from the mean
• Ex: golf scores of erratic golfer or consistent golfer
Standard Deviation• Statistical measure of variability in a group of
scores• A single # that tells how the scores in a
frequency distribution are dispersed around the mean
Normal Distribution
Standard Deviation
1212121212
20 22021 22122 22223 223
Correlation
DOES NOT IMPLY CAUSATION!
Correlation: Two variable are related to each other with no causation
• The strength of the correlation is defined with a statistic called the correlation coefficient (+1.00 to -1.00)
• Positive- Indicates the two variables go in the same direction
• EX: High school & GPA
CorrelationPositive• two variables go in the
same direction• EX: High school & GPA
Negative• two variable that go in
the opposite directions• EX: Absences & Exam
scores
Graphing Correlations- Scatter Plot
No Correlation- Illusory
Strength of the Correlation ( r)
• Correlation Coefficent- Numerical index of the degree of relationship between two variable or the strength of the relationship.
• Coefficient near zero = no relationship between the variables ( one variable shows no consistent relationship to the other 50%)
• Perfect correlation of +/- 1.00 rarely ever seen• Positive or negative ONLY indicate the direction,
NOT the strength
Coefficient of Determination-Index of correlation’s predictive power
• Percentage of variation in one variable that can be predicted based on the other variable
• To get this number, multiply the correlation coefficient by itself
• EX: A correlation of .70 yields a coefficient of determination of .49 (.70 X .70= .49) indicating that variable X can account for 49% of the variation in variable Y
• Coefficient of determination goes up as the strength of a correlation increases (B.11)
Inferential Statistics
• The purpose is to discover whether the finding can be applied to the larger population from which the sample was collected.
• P-value= .05 for statistical significance.
• 5% likely the results are due to chance.
Null Hypothesis
• Is the observed correlation large enough to support our hypothesis or might a correlation of the size have occurred by chance?
• Do our result REJECT the null hypothesis?
Statistical Significance
• It is said to exist when the probability that the observed findings are due to chance is very low, usually less than 5 chances in 100 (p value = .05 or less)
• When we reject our null hypothesis we conclude that our results were statistically significant.
Type I v. Type II Error
• Type I Error- said IV had an effect but it didn’t– False alarm
• Type II Error- don’t believe the IV had an effect but it really does
• Which is worse?