Statistics

Descriptive Statistics Organize & summarize data (ex: central tendency & variability

Scales of Measurement Nominal Categories for classifying Least informative scale EX: 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 SkewedNegatively 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

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

Correlation Positive 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 +/ 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?