Research Design Quantitative Data Analysis PADMN 6289// WEEK 10

Examining relationships 03 Descriptive stats 02 Quantitative data recap 01 This Videocast

Quantitative Data Recap 01

Quantitative Data Information that is systematically collected and communicated in numerical form; Data that can be analyzed with mathematical (usually statistical) techniques

Levels of Measurement Nominal (aka Categorical) Ordinal Interval Ratio Descriptive labels/ categories; no meaningful order to values Depict the order of a measurement, but not the difference between integers Depict the order and difference between integers (“interval” = distance between entities); No “true” zero Depict the order and difference between integers; “True” zero ✓ Genders ✓ Countries ✓ Cities ✓ Occupations ✓ Likert-scale survey responses ✓ “Star” ratings ✓ Interval/ratio data expressed as categories ✓ IQ Scores ✓ Temperature ✓ Age ✓ Income ✓ Budgets

Descriptive Statistics 02

Descriptive Statistics Analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.

Counts Percentages Rates Ratios Measures of central tendency Measures of dispersion Commonly Used Descriptive Statistics

Mean: Average value (sum/n) Median: Midpoint of a distribution (middle number) Mode: Most frequent value Measures of Central Tendency Figures (numbers) that represent the “center” of the data

Levels of Measurement Nominal (aka Categorical) Ordinal Interval Ratio Descriptive labels/ categories; no meaningful order to values Depict the order of a measurement, but not the difference between integers Depict the order and difference between integers (“interval” = distance between entities); No “true” zero Depict the order and difference between integers; “True” zero ✓ Mode ✓ Mode ✓ Median ✓ Mode ✓ Median ✓ Mean ✓ Mode ✓ Median ✓ Mean

Measures of Central Tendency $75k $65k $50k $50k $30k $30k $30k Mode = $30k

Measures of Central Tendency $75k $65k $50k $50k $30k $30k $30k Median = $50k Mode = $30k

Measures of Central Tendency $75k $65k $50k $50k $30k $30k $30k Mean = $47k Median = $50k Mode = $30k

Measures of Central Tendency $75k $65k $50k $50k $30k $30k $30k Mean = $47k Median = $50k Mode = $30k $500k $75k $65k $50k $50k $30k $30k $30k Mean = $104k Median = $50k Mode = $30k

Range: Difference between lowest and highest values Standard Deviation: Calculated spread from the mean Interquartile Range: Spread from the median (Q3-Q1) Measures of Dispersion “Spread” of data; how far the data diverge from the data “center”

Levels of Measurement Nominal (aka Categorical) Ordinal Interval Ratio Descriptive labels/ categories; no meaningful order to values Depict the order of a measurement, but not the difference between integers Depict the order and difference between integers (“interval” = distance between entities); No “true” zero Depict the order and difference between integers; “True” zero ✓ Mode ✓ Mode ✓ Median ✓ Interquartile range ✓ Mode ✓ Median ✓ Mean ✓ Interquartile range ✓ Standard deviation ✓ Mode ✓ Median ✓ Mean ✓ Interquartile range ✓ Standard deviation

Visualizing Data Strongly agree = 5 Agree = 4 Neither agree nor disagree = 3 Disagree = 2 Strongly disagree = 1 Mean = 3.13 Mode = 5 Mean = 3.16 Mode = 3 Indicate your level of agreement that this is an overall effective course...

Examining Relationships 03

Examining Relationships Differences in measures of central tendency (means, medians, modes)

$75k $65k $50k $50k $30k $30k $30k Mean = $47k Median = $50k Mode = $30k $500k $75k $65k $50k $50k $30k $30k $30k Mean = $104k Median = $50k Mode = $30k

Examining Relationships Differences in measures of central tendency (means, medians, modes) Crosstabs

Differences in satisfaction with city services based on race Using frequencies Satisfied Neither Dissatisfied Total White 113 30 8 151 Nonwhite 37 15 22 74 Using percentages Satisfied Neither Dissatisfied Total White 75 20 5 100 Nonwhite 50 20 30 100

Examining Relationships Differences in measures of central tendency (means, medians, modes) Crosstabs • Controlling for a third variable in crosstabs

Differences in satisfaction with city services based on race (percentages) Satisfied Neither Dissatisfied Total White 75 20 5 100 Nonwhite 50 20 30 100

Differences in satisfaction with city services based on race (percentages) Less- affluent neighborhoods Satisfied Neither Dissatisfied Total White 28 22 50 100 Nonwhite 31 18 51 100 More-affluent neighborhoods Satisfied Neither Dissatisfied Total White 77 18 5 100 Nonwhite 74 20 6 100

Examining Relationships Differences in measures of central tendency (means, medians, modes) Crosstabs • Controlling for a third variable in crosstabs Measures of association • Appropriate correlation analysis for level of measurement (i.e. nominal, ordinal, interval); Johnson, pg. 208 • Direction of relationship • Strength of relationship (correlation coefficient = r); Johnson, pg. 206

Hours studying Classes attended (stronger relationship) (weaker relationship) GPA GPA

GPA Hours studying GPA Hours partying (positive relationship) (negative relationship)

Research Design Quantitative Data Analysis PADMN 6289// WEEK 10