Descriptive Statistics

1. 14 Descriptive Statistics

2. Learning Objectives • Recognize Statistical Symbols For Population Parameters And Sample Statistics • Identify The Two Broad Classifications Of Statistics • Discuss Four Major Groups Of Descriptive Statistics

3. Learning Objectives Compare Categories Within Each Of The Four Major Groups Of Descriptive Statistics Determine Appropriate Descriptive Statistics To Use In Presenting Selected Data Construct Graphs To Present Selected Descriptive Statistics

4. Learning Objectives Critique Descriptive Statistics Presented In Research Reports

5. Learning Objective OneRecognize Statistical Symbols For Population Parameters And Sample Statistics

6. Statistical Terms • Parameters used when discussing populations • Statistics used when discussing samples

7. Determining Type of Statistical Data • Greek letter mu (μ)—population parameters • English letters s or SD—sample statistics

8. Trends in Literature • Words instead of symbols • mean or standard deviation

9. Learning Objective TwoIdentify The Two Broad Classifications Of Statistics

10. Descriptive Statistics • Organize and summarize numerical data collected from samples • Allows examination of study participants’ • Characteristics • Behaviors • Experiences

11. Inferential Statistics • Concerned with populations • Use sample data to make inferences about a population • Help determine real differences versus chance differences

12. Descriptive VersusInferential Statistics • Descriptive—examine characteristics of study participants • Inferential—determine if sample is representative of population

13. Learning Objective ThreeDiscuss Four Major Groups Of Descriptive Statistics

14. Descriptive Statistics • Measures to condense data • Measures of central tendency • Measures of variability • Measures of relationships

15. Measures to Condense Data • Summarize data • Frequency distributions • Graphic presentations • Percentages

16. Measures of Central Tendency • Average distribution or most common value for a group of data • Mean • Mode • Median

17. Measures of Variability • Describe how spread out the values are in a distribution • Range • Percentile • Standard deviation • Variance • Z scores

18. Measures of Relationships • Concern the correlations between variables • Correlation coefficients • Scatter plots • Contingency tables • Correlational procedures

19. Learning Objective FourCompare Categories Within EachOf The Four Major GroupsOf Descriptive Statistics

20. Measures to Condense Data • Frequency distribution • All values or scores are listed. • Number of times each one appears is recorded.

21. Measures to Condense Data—Frequency Distribution • Distribution is small. • Score listed individually • Range of scores is large. • Group the scores before counting frequencies • The groups of scores are called class intervals.

22. Measures to Condense Data—Frequency Distribution (cont’d) • Symmetrical distributions • Skewed, or nonsymmetrical, distributions • Positively skewed • Negatively skewed

23. Measures to Condense Data—Frequency Distribution (cont’d) • Normal distribution • Symmetrical distribution • One set of values in the middle of the distribution • Bell-shaped curve

24. Measures to Condense Data—Graphic Presentations • Data may be presented in a graphic form. • Visually appealing • According to the level of measurement of the variable to be presented

25. Measures to Condense Data—Graphic Presentations (cont’d) • Bar graph • Represents frequency of occurrence • Illustrates distribution of nominal data and some types of ordinal data • Histogram • Graph that uses bars to represent the frequency distribution of a variable • Illustrates variables measured at the ordinal, interval, or ratio level

26. Measures to Condense Data—Graphic Presentations • Frequency polygon • Graph using dots connected with straight lines • Represents frequency distribution of ordinal, interval, or ratio data

27. Measures to Condense Data—Percentages • Number of parts per hundred that a certain portion of the whole represents • Statistic representing the proportion of a subgroup to a total group • Expressed as a percentage ranging from 0 to 100

28. Measures of Central Tendency • Mode (Mo) • Category or value that occurs most often • Modal class • Category with the greatest frequency • Unimodal • Bimodal • Multimodal

29. Measures of Central Tendency (cont’d) • Median (Md or Mdn) • Middle score or value • Mean (M or ˆ “x-bar”) • Average sum of a set of values x

30. Measures of Variability • Range • Distance between highest and lowest value • Interquartile range (IQR) • Middle half of the values • Semiquartile range (SQR) • Half the interquartile range

31. Measures of Variability (cont’d) • Percentile • Datum point below which lies a certain percentage of the values • Common statistic used to compare performance with others

32. Measures of Variability (cont’d) • Standard deviation (SD or s) • Measurement that indicates the average variation of all the values in a set from the mean value

33. Measures of Variability (cont’d) • Variance • Measure used in several inferential statistical tests • Z score • Score indicating how many standard deviations from the mean a value lies • Interpreted in relation to SD units above or below the mean

34. Measures of Relationships • Correlation coefficient (r) • Magnitude and direction of relationship between two variables • Can vary between –1.00 and ++1.00 • Zero (0) indicates the absence of any relationship.

35. Measures of Relationships (cont’d) • Positive relationship • Two variables tend to increase or decrease together. • Negative relationship • As one variable increases, the other variable tends to decrease.

36. Measures of Relationships (cont’d) • Correlation does not mean causation.

37. Measures of Relationships—Correlation Coefficient • No set criteria to evaluate the actual strength of a correlation coefficient • Nature of variables being studied help determine the strength of the relationship. • Coefficient of determination • Obtained by squaring the correlation coefficient (r2) • Interpreted as percentage of variance shared by two variables

38. Measures of Relationships (cont’d) • Scatter plot • Graphic presentation of the relationship between two variables • Determines magnitude of the relationship and the direction of the relationship • Negative correlation • Perfect positive correlation • No relationship between the two variables

39. Measures of Relationships (cont’d) • Contingency table • Means of visually displaying relationship between sets of data

40. Measures of Relationships (cont’d) • Correlational procedures • Pearson product-moment correlation (Pearson r) • Spearman rho (rs, rrho, or rho)

41. Learning Objective FiveDetermine Appropriate Descriptive Statistics To Use In Presenting Selected Data

42. Frequency Distribution • Appropriate measure to condense data for reporting all level of data • Nominal • Ordinal • Interval • Ratio

43. Mode • Only measure of central tendency appropriate for nominal data

44. Median • Appropriate measure of central tendency for ordinal, interval, and ratio data

45. Mean • Appropriate for interval and ratio data • Considered the most stable measure of central tendency if distribution is normal

46. Standard Deviation • Most widely used measure of variability when interval or ratio data are obtained

47. Variance • Discussed infrequently as a measure of variability in descriptive statistics • Not in the same unit of measurement as the variable that is being examined

48. Z Score • Useful statistic for interpreting a particular value in relation to other distribution values • Allows performance comparison of someone on nonequivalent tests as a measure of variability

49. Measures of Relationships—Correlational Procedures • Pearson r • Used when both sets of data are at the interval or ratio level • Spearman rho • Used with ordinal data

50. Measures of Relationships—Correlational Procedures • Correlational procedures appropriate for nominal data include • Contingency coefficient • Phi coefficient • Cramer’s V