Statistics

1. Statistics

2. Review of Statistics Levels of Measurement Descriptive and Inferential Statistics

3. Qualitative Data Nominal Ordinal Quantitative Data Interval Ratio Levels of MeasurementNature of the variable affects rules applied to its measurement

4. Nominal Measurement • Lowest Level • Sorting into categories • Numbers merely symbols--have no quantitative significance • Assign equivalence or nonequivalence Examples, gender, marital status, etc

5. Male / female smoker /nonsmoker alive/dead 1 2 nominal

6. Rules of Nominal system • All of members of one category are assigned same numbers • No two categories are assigned the same number (mutual exclusivity) • Cannot treat the numbers mathematically • Mode is the only measure of central tendency

7. The Ordinal Scale • Sorting variations on the basis of their relative standing to each other • Attributes ordered according to some criterion (e.g. best to worst) • Intervals are not necessarily equal Should not treat mathematically, frequencies and modes ok

8. Ordinal scale 0 1 2 3 4

9. Interval Scale • Researcher can specify rank ordering of variables and distance between • Intervals are equal but no rational zero point (example IQ scale, Fahrenheit scale) • Data can be treated mathematically, most statistical tests are possible

10. Ratio Scale • Highest level of measurement • Rational meaningful zero point • Absolute magnitude of variable (e.g., mgm/ml of glucose in urine) • Ideal for all statistical tests

11. Descriptive Statistics Used to describe data • Frequency distributions, histograms, polygons • Measures of Central Tendency • Dispersion • Position within a sample

12. Frequency Distributions Imposing some order on a mass of numerical data by a systematic arrangement of numerical values from lowest to highest with a count of the number of times each value was obtained--Most frequently represented as a frequency polygon

13. Frequency distribution

14. Shapes of distributions • Symmetry • Modality • Kurtosis

15. Symmetry • Normal curve symmetrical • If non symmetrical skewed (peak is off center) • positively skewed • negatively skewed

16. Positive skew

17. Negative skew

18. Modality • Describes how many peaks are in the distribution • unimodal • bimodal • multimodal

19. unimodal

20. bimodal

21. multimodal

22. Kurtosis • Peakedness of distribution • platykurtic • mesokurtic • leptokurtic

23. Mesokurtic

24. Platykurtic

25. Leptokurtic

26. Measures of Central Tendency Overall summary of a group’s characteristics “What is the average level of pain described by post hysterectomy pts.?” “How much information does the typical teen have about STDs?”

27. Mean • Arithmetic average • Most widely reported meas. of CT • Not trustworthy on skewed distributions

28. Median • The point on a distribution above which 50% of observations fall • Shows how central the mean really is since the median is the number which divides the sample in half • Does not take into account the quantitative values of individual scores • Preferred in a skewed distribution

29. Mode • The most frequently occuring score or number value within a distribution • Not affected by extreme values • Shows where scores cluster • There may be more than one mode in a distribution • Arrived at through inspection • limited usefulness in computations

30. Which measures of central tendency is represented by each of these lines?

31. Variability or Dispersion Measures • Percentile rank-the point below which a % of scores occur • Range --highest-lowest score • Standard deviation--master measure of variability--average difference of scores from the mean--allows one to interpret a score as it relates to others in the distribution

32. Normal (Gaussian) Distribution • Mathematical ideal • 68.3% of scores within +/- 1sd • 95.4% of scores within +/- 2sd • 99.7% of scores within +/- 3sd unimodal mesokurtic symmetrical

33. Normal curve  1% 13.5% 34% 34% 13.5 % 1 % 

34. Inferential Statistics Used to make inferences about entire population from data collected from a sample Two classifications based on their underlying assumptions • Parametric • Nonparametric

35. Parametric • Based on population parameters • Have numbers of assumptions (requirements) • Level of measurement must be interval or ratio • t-test • Pearson product moment correlation ® • ANOVA • Multiple regression analysis

36. Parametric • Preferable because they are more powerful--better able to detect a significant result if one exists.

37. Nonparametric • Not as powerful • Have fewer assumptions • Level of measurement is nominal or ordinal • Chi squared

38. Some examples of Statistical tests and their use

40. Hypothesis testing • Research Hypothesis Hr--Statement of the researcher’s prediction • Alternate Hypothesis Ha--Competing explanation of results • Null Hypothesis Ho -- Negative Statement of hypothesis tested by statistical tests

41. Research Hypotheses • Method A is more effective than method B in reducing pain (directional) • Method A will differ from Method B in pain reducing effectiveness (nondirectional)

42. Null Hypothesis • Method A equals Method B in pain reduction effectiveness.(any difference is due to chance alone This must be statistically tested to say that something else beside chance is creating any difference in results

43. Type I and Type II errors • Type I--a decision to reject the null hypothesis when it is true. A researcher conludes that a relationship exists when it does not. • Type II--a decisioon to accept the null hypothesis when it is false. The researcher concludes no relationship exists when it does.

44. Level of Significance • Degree of risk of making a Type one error. (saying a treatment works when it doesn’t or that a relationship exists when there is none) • Signifies the probability that the results are due to chance alone. • p=.05 means that the probability of the results being due to chance are 5%