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Statistics

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

yardley-shannon
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Statistics

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  1. Statistics

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

  3. 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

  4. 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

  5. Frequency Distribution

  6. Histogram & Frequency Polygon • X axis- possible scores • Y axis- frequency

  7. Normal Curve of Distribution • Bell-shaped curve • Absolutely symmetrical • Central Tendency: mode, mean, median?

  8. Central Tendency Let’s look at the salaries of the employees at Dunder Mifflen Paper in Scranton: • 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 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.

  9. Skewed Distributions Positively Skewed Negatively Skewed

  10. 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 Bimodal Distribution

  11. 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

  12. 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

  13. Normal Distribution

  14. Standard Deviation 12 12 12 12 12 20 220 21 221 22 222 23 223

  15. Correlation DOES NOT IMPLY CAUSATION!

  16. 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

  17. 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

  18. Graphing Correlations- Scatter Plot

  19. No Correlation- Illusory

  20. 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

  21. 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)

  22. 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.

  23. 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?

  24. 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.

  25. 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?

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