DESCRIPTIVE STATISTICS & DATA PRESENTATION*

Transcription

1 Level 1 Level 2 Level 3 Level evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department basommer@ucdavis.edu Instructions: This is a practice review, based on Ch. 18 which must be read and understood first. Have a pencil and some scratch paper on hand as you go through this. When you see a statement or question in blue, try to answer or anticipate the information before you bring it onscreen. You can use the right-pointing arrow key on your keyboard to move forward and the left-pointing arrow to move back. At the top menu in Acrobat Reader, select Window > Show bookmarks. A menu bar will appear on the left and permit you to directly access a section - useful for review. * permission granted for educational use only, please credit the source.

2 Contents

3 Definitions & use Contents

4 Contents Definitions & use Selecting appropriate statistics

5 Contents Definitions & use Selecting appropriate statistics Specify variables

6 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous?

7 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes

8 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables

9 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes

10 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes Central tendency

11 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes Central tendency Variability, dispersion

12 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes Central tendency Variability, dispersion What is a standard deviation?

13 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes Central tendency Variability, dispersion What is a standard deviation? Why bother with descriptive statistics?

14 Contents Definitions & use Selecting appropriate statistics Specify variables Is outcome categorical or continuous? Descriptive statistics for categorical outcomes Percentages based on contingency tables Descriptive statistics for continuous outcomes Central tendency Variability, dispersion What is a standard deviation? Why bother with descriptive statistics? To provide a quantitative description of a SAMPLE

15 DEFINITIONS

16 DEFINITIONS group of interest to researcher

17 DEFINITIONS group of interest to researcher POPULATION

18 DEFINITIONS group of interest to researcher POPULATION subset of a population

19 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE

20 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE quantitative characteristic of a population

21 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE quantitative characteristic of a population PARAMETER!

22 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE quantitative characteristic of a population PARAMETER! quantitative characteristic of a sample

23 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE quantitative characteristic of a population PARAMETER! quantitative characteristic of a sample STATISTIC

24 DEFINITIONS group of interest to researcher POPULATION subset of a population SAMPLE quantitative characteristic of a population PARAMETER! quantitative characteristic of a sample STATISTIC Commit these to memory right now.

25 Define: STATISTIC

26 Define: STATISTIC quantitative characteristic of a sample

27 Define: STATISTIC quantitative characteristic of a sample SAMPLE

28 Define: STATISTIC quantitative characteristic of a sample SAMPLE subset of a population

29 Define: STATISTIC quantitative characteristic of a sample SAMPLE subset of a population POPULATION

30 Define: STATISTIC quantitative characteristic of a sample SAMPLE subset of a population POPULATION group of interest to researcher

31 Define: STATISTIC quantitative characteristic of a sample SAMPLE subset of a population POPULATION group of interest to researcher PARAMETER!

32 Define: STATISTIC quantitative characteristic of a sample SAMPLE subset of a population POPULATION group of interest to researcher PARAMETER! quantitative characteristic of a population

33 Choosing the correct descriptive statistics - KEY question

34 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous?

35 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable.

36 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL

37 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples:

38 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples:

39 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples: or

40 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples: or YES

41 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples: or YES NO

42 Choosing the correct descriptive statistics - KEY question Is the OUTCOME (Dependent variable) categorical or continuous? If the levels/values of the variable in question differ in quality or kind, then it is a? variable. Ans: CATEGORICAL Examples: or YES NO DON T KNOW

43 CONTINUOUS VARIABLES are those whose levels or values vary.

44 CONTINUOUS VARIABLES are those whose levels or values vary. Ans: along a quantitative dimension

45 CONTINUOUS VARIABLES are those whose levels or values vary. Ans: along a quantitative dimension Examples:

46 CONTINUOUS VARIABLES are those whose levels or values vary. Ans: along a quantitative dimension Examples: Number of hours spent watching TV

47 CONTINUOUS VARIABLES are those whose levels or values vary. Ans: along a quantitative dimension Examples: Number of hours spent watching TV Enjoyment - on a scale of 1 to 10

48 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down.

49 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables

50 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down.

51 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is...

52 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER

53 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels?

54 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female

55 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female Dependent Variable (outcome)?

56 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female Dependent Variable (outcome)? LEG CROSS

57 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female Dependent Variable (outcome)? LEG CROSS Levels?

58 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female Dependent Variable (outcome)? LEG CROSS Levels? Yes (within 30 seconds) No (> 30 seconds or not at all)

59 EXAMPLE: the Reasoner Hypothesis: A woman crosses her legs within 30 seconds of sitting down. Examine hypothesis or question and specify variables The hypothesis implies that men do not cross their legs within 30 seconds of sitting down. The condition in question (the predictor or independent variable) is... GENDER Levels? male female Dependent Variable (outcome)? LEG CROSS Levels? Yes (within 30 seconds) No (> 30 seconds or not at all) Note: these are operational definitions

60 Is the independent (predictor) variable categorical or continuous?

61 Is the independent (predictor) variable categorical or continuous? The levels of gender are male and female. These are discrete categories, therefore gender is categorical.

62 Is the independent (predictor) variable categorical or continuous? The levels of gender are male and female. These are discrete categories, therefore gender is categorical. Is the dependent variable (outcome) categorical or continuous?

63 Is the independent (predictor) variable categorical or continuous? The levels of gender are male and female. These are discrete categories, therefore gender is categorical. Is the dependent variable (outcome) categorical or continuous? The levels of leg cross are yes and no. These are discrete categories, therefore in this example, the dependent variable, leg cross, is categorical.

64 Is the independent (predictor) variable categorical or continuous? The levels of gender are male and female. These are discrete categories, therefore gender is categorical. Is the dependent variable (outcome) categorical or continuous? The levels of leg cross are yes and no. These are discrete categories, therefore in this example, the dependent variable, leg cross, is categorical. What if the outcome were measured in time (minutes and seconds) rather than YES vs. NO?

65 Is the independent (predictor) variable categorical or continuous? The levels of gender are male and female. These are discrete categories, therefore gender is categorical. Is the dependent variable (outcome) categorical or continuous? The levels of leg cross are yes and no. These are discrete categories, therefore in this example, the dependent variable, leg cross, is categorical. What if the outcome were measured in time (minutes and seconds) rather than YES vs. NO? In that case the dependent variable would be a continuous measure.

66 Your research assistant has collected observational data. Now it is up to you to make sense of it.

67 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example:

68 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: cells

69 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. cells

70 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. GENDER female male cells

71 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells

72 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male 232 cells

73 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells

74 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells

75 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells

76 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells margins (totals)

77 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells 361 margins (totals)

78 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. CROSS within 30 seconds Yes No GENDER female male cells margins (totals)

79 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. GENDER female male CROSS within 30 seconds Yes No cells margins (totals)

80 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. GENDER female male CROSS within 30 seconds Yes No cells margins (totals)

81 Your research assistant has collected observational data. Now it is up to you to make sense of it. The first step is to enter each COUNT in the appropriate cell on a CONTINGENCY TABLE. Here is an example: Put the independent variable (predictor) along the top, and the dependent variable (outcome) along the side. GENDER female male CROSS within 30 seconds Yes No cells margins (totals) N = 708 (check to see that the marginal totals add up correctly)

82 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult.

83 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell.

84 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. cell

85 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. cell

86 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. cell margins

87 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. Where does the independent (or predictor) variable and its levels belong? cell margins

88 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. Where does the independent (or predictor) variable and its levels belong? PREDICTOR Variable (INDEPENDENT Variable) Level 1 Level 2 cell margins

89 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. Where does the independent (or predictor) variable and its levels belong? And the outcome (dependent variable)? PREDICTOR Variable (INDEPENDENT Variable) Level 1 Level 2 cell margins

90 The General Case - contingency tables can have 2 or more columns and rows. Beyond 4 or 5 of either makes interpretation difficult. On the table below, indicate a cell. And a margin. Where does the independent (or predictor) variable and its levels belong? And the outcome (dependent variable)? OUTCOME (Dependent variable) PREDICTOR Variable (INDEPENDENT Variable) Level 1 Level 2 Level 1 Level 2 cell margins Level 3

91 Returning to the Reasoner data N = 708

92 Returning to the Reasoner data N = 708 CROSS within 30 Yes seconds GENDER female male No

93 Returning to the Reasoner data N = 708 CROSS within 30 Yes seconds GENDER female male No The contingency table shows the raw data. You need to refine it a bit more for presentation.

94 A good way to summarize counts such as these is to transform them into?.

95 A good way to summarize counts such as these is to transform them into?. PERCENTAGES

96 A good way to summarize counts such as these is to transform them into?. PERCENTAGES Make a table showing the results using percentages (calculate from preceding slide).

97 A good way to summarize counts such as these is to transform them into?. PERCENTAGES Make a table showing the results using percentages (calculate from preceding slide). Table 1 Percentage of women and men who crossed their legs within 30 seconds of sitting down. Women Men (n = 361) (n = 347) 64.3% 27.7%

98 A good way to summarize counts such as these is to transform them into?. PERCENTAGES Make a table showing the results using percentages (calculate from preceding slide). Table 1 Percentage of women and men who crossed their legs within 30 seconds of sitting down. Women Men (n = 361) (n = 347) 64.3% 27.7% Note: The percentages are the descriptive statistics.

99 A good way to summarize counts such as these is to transform them into?. PERCENTAGES Make a table showing the results using percentages (calculate from preceding slide). Table 1 Percentage of women and men who crossed their legs within 30 seconds of sitting down. Women Men (n = 361) (n = 347) 64.3% 27.7% Note: The percentages are the descriptive statistics. A descriptive statistic is.

100 A good way to summarize counts such as these is to transform them into?. PERCENTAGES Make a table showing the results using percentages (calculate from preceding slide). Table 1 Percentage of women and men who crossed their legs within 30 seconds of sitting down. Women Men (n = 361) (n = 347) 64.3% 27.7% Note: The percentages are the descriptive statistics. A descriptive statistic is. Ans: A quantitative characteristic of a sample.

101 A narrative description can be used within report or talk. State the results in words.

102 A narrative description can be used within report or talk. State the results in words. Sixty-four percent of the women (n = 361) and 28 percent of the men (n = 347) crossed their legs within 30 seconds of sitting down.

103 Draw a graph of the results.

104 Draw a graph of the results. %

105 Draw a graph of the results. % Women GENDER

106 Draw a graph of the results. % Women Men GENDER

107 Draw a graph of the results. % Women Men GENDER Figure 1. Percent of women (n=361) and men (n=347) crossing within 30 seconds.

108 Draw a graph of the results. % Women Men GENDER Figure 1. Percent of women (n=361) and men (n=347) crossing within 30 seconds. Note: Using APA style, table titles are placed above the table, and figure titles are placed below the figure.

109 You would not use all three in a single report. Pick the one that best illustrates your findings.

110 You would not use all three in a single report. Pick the one that best illustrates your findings. Here is another example using additional data.

111 You would not use all three in a single report. Pick the one that best illustrates your findings. Here is another example using additional data. Table 2 Of those who crossed their legs, percentage showing each type of cross, by gender. Gender Type! Women! Men! (n=252)! (n=122) Knee-to-knee! 50.4! 9.0 Ankle-to-ankle! 17.1! 49.2 Ankle-to-knee! 10.3! 26.2 Cross-legged! 19.8! 13.9 Other! 2.4! 1.6

112 You would not use all three in a single report. Pick the one that best illustrates your findings. Here is another example using additional data. Table 2 Of those who crossed their legs, percentage showing each type of cross, by gender. Gender Type! Women! Men! (n=252)! (n=122) Knee-to-knee! 50.4! 9.0 Ankle-to-ankle! 17.1! 49.2 Ankle-to-knee! 10.3! 26.2 Cross-legged! 19.8! 13.9 Other! 2.4! 1.6 Note that the sample sizes (n) are provided so that the reader could reconstruct the actual numbers.

113 When outcome variable is CONTINUOUS,

114 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam,

115 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]?

116 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central

117 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central Ans: central tendency and variability.

118 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central Ans: central tendency and variability. What are the three measures of central tendency?

119 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central Ans: central tendency and variability. What are the three measures of central tendency? Mean

120 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central Ans: central tendency and variability. What are the three measures of central tendency? Mean Median

121 When outcome variable is CONTINUOUS, for example, enjoyment - on a scale of 1 to 10, or score on an exam, what two major aspects of the data need to be described [in addition to the sample size (N)]? Hint: One begins with central Ans: central tendency and variability. What are the three measures of central tendency? Mean Median Mode

122 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3

123 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top.

124 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X

125 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol.

126 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size

127 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7

128 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol)

129 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol) = 2

130 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol) = 2 Median

131 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol) = 2 Median Mdn = 4

132 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol) = 2 Median Mean Mdn = 4

133 EXAMPLE: Scores on a 10-point quiz: Scores are 2, 10, 6, 2, 4, 8, 3 Put them in order with the proper label at the top. X Calculate the following and also show the appropriate statistical symbol. Sample size N = 7 Mode (no symbol) = 2 Median Mdn = 4 Mean M or X = 5

134 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2

135 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median?

136 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median? Mdn = 4

137 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median? Mdn = 4 If you didn t get it right, make a list of all of the individual scores.

138 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median? Mdn = 4 If you didn t get it right, make a list of all of the individual scores. X

139 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median? Mdn = 4 If you didn t get it right, make a list of all of the individual scores. X Find the middle score. That will be the median.

140 Here is another set of scores. These have frequencies (f) listed -- meaning that there might be more than one of any given score. X! f 10! 1 9! 0 8! 1 7! 0 6! 1 5! 0 4! 1 3! 1 2! 2 Median? Mdn = 4 If you didn t get it right, make a list of all of the individual scores. X Find the middle score. That will be the median.

141 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency.

142 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is

143 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY

144 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores.

145 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores. SPREAD or DISPERSION

146 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores. SPREAD or DISPERSION Two indicators of variability are

147 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores. SPREAD or DISPERSION Two indicators of variability are Range Standard Deviation (SD)

148 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores. SPREAD or DISPERSION Two indicators of variability are Range Standard Deviation (SD) Calculate the range of these scores. X

149 Recap: We are reviewing necessary descriptive statistics for continuous variables. The first aspect of describing quantitative findings along a continuous variable is central tendency. The other important aspect is VARIABILITY Variability refers to the of the scores. SPREAD or DISPERSION Two indicators of variability are Range Standard Deviation (SD) Calculate the range of these scores. X Range = 10-2 = 8

150 What is so special about the standard deviation?

151 What is so special about the standard deviation? It shows how closely scores group around the mean.

152 What is so special about the standard deviation? It shows how closely scores group around the mean. As a set of scores become more spread out from the mean, the standard deviation (increases or decreases?)

153 What is so special about the standard deviation? It shows how closely scores group around the mean. As a set of scores become more spread out from the mean, the standard deviation (increases or decreases?) Increases. Larger SD = greater variability

154 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X

155 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M)

156 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5

157 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3

158 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1

159 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1

160 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2

161 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3

162 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3

163 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them.

164 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M) 2 25

165 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

166 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

167 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

168 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

169 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

170 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

171 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

172 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M)

173 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M) =

174 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M) = average of the This is a sort of spread (squared).

175 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M) = average of the This is a sort of spread (squared). Unsquare it (take square root) =

176 What is the Standard Deviation? Here is the long way to calculate it (so you can see where it comes from). Using the formula is easier. M = 5 X (X-M) - 5 = 5-5 = 3-5 = 1-5 = -1-5 = -2-5 = -3-5 = -3 Note that each individual score is being subtracted from the mean. We can t do much with these numbers because if we add them, they will total 0. That is the nature of the mean. A solution is to square each difference score, and then add them. (X-M) = average of the This is a sort of spread (squared). Unsquare it (take square root) = 2.88 = SD

177 Some Greek

178 Some Greek Σ =

179 Some Greek Σ = Sum of

180 Some Greek Σ = Sum of σ =

181 Some Greek Σ = Sum of σ = standard deviation for the population

182 Some Greek Σ = Sum of σ = standard deviation for the population Standard deviation can also be abbreviated as SD or StDev

183 Some Greek Σ = Sum of σ = standard deviation for the population Standard deviation can also be abbreviated as SD or StDev Formula for the standard deviation

184 Some Greek Σ = Sum of σ = standard deviation for the population Standard deviation can also be abbreviated as SD or StDev Formula for the standard deviation = ΣΧ 2 (ΣΧ) 2 Ν Ν 1

185 Some Greek Σ = Sum of σ = standard deviation for the population Standard deviation can also be abbreviated as SD or StDev Formula for the standard deviation = ΣΧ 2 (ΣΧ) 2 Ν Ν 1 Calculators often have 2 formulas for the Standard Deviation, one for the sample (shown as N or s) and the other for the population (shown as N-1 or σ). Use the population (N-1or σ) formula.

186 List three symbols or abbreviations for the standard deviation

187 List three symbols or abbreviations for the standard deviation σ SD StDev

188 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?).

189 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX

190 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX Add up the scores.

191 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX Add up the scores. ΣΧ 2

192 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX Add up the scores. ΣΧ 2 Square each score and then add them.

193 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX Add up the scores. ΣΧ 2 Square each score and then add them. (ΣΧ) 2

194 List three symbols or abbreviations for the standard deviation σ SD StDev Describe each of the following arithmetic operations (i.e., how do you calculate these?). ΣX Add up the scores. ΣΧ 2 Square each score and then add them. (ΣΧ) 2 Add the scores and then square the total.

195 Fill-in the proper statistic.

196 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include.

197 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size)

198 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size) In most cases, also provide the and the.

199 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size) In most cases, also provide the and the. Mean... Standard Deviation

200 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size) In most cases, also provide the and the. Mean... Standard Deviation If the distribution of scores is skewed (see textbook), then use the and the.

201 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size) In most cases, also provide the and the. Mean... Standard Deviation If the distribution of scores is skewed (see textbook), then use the and the. Median... Range

202 Fill-in the proper statistic. When describing an outcome based on a continuous variable, always include. N (sample size) In most cases, also provide the and the. Mean... Standard Deviation If the distribution of scores is skewed (see textbook), then use the and the. Median... Range Only use the Standard Deviation when presenting the Mean (no SD with the Median or Mode).

203 Here are the students results for a 10-point quiz described earlier. N = 7 M = 5 SD = 2.88

204 Here are the students results for a 10-point quiz described earlier. N = 7 M = 5 SD = 2.88 How would you state these results in a research report?

205 Here are the students results for a 10-point quiz described earlier. N = 7 M = 5 SD = 2.88 How would you state these results in a research report? Seven students took a 10-point quiz (M=5, SD = 2.88). or The mean for the 10-point quiz was 5 (N=7, SD = 2.88)

206 REVIEW

207 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics.

208 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Descriptive statistics

209 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Descriptive statistics Categorical

210 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Categorical Descriptive statistics Percentages based on numbers in contingency table

211 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Categorical Descriptive statistics Percentages based on numbers in contingency table Continuous

212 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Categorical Continuous Descriptive statistics Percentages based on numbers in contingency table Mean & Standard Deviation

213 REVIEW Examine outcome variable (dependent variable) and select the proper descriptive statistics. Outcome variable! Categorical Continuous Descriptive statistics Percentages based on numbers in contingency table Mean & Standard Deviation Always include