Elementary Quantitative Analysis

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Elementary Quantitative Analysis

• A/S 305 Social Research Methods
• Sarah Goodrum, Ph.D.

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Elementary Quantitative Analysis

• Univariate Analysis
• Bivariate Analysis

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Univariate Analysis

• analysis of one variable
• e.g., gender
• e.g., income

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Univariate Analysis

• Frequency Table
• Frequency Distribution tally up the number of
  cases in each category of the variable
• Percent Distribution divide each cell by the
  total of cases and multiply by 100 (its easier
  to compare distribution than frequency
  distribution)

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Frequency Distribution of General Happiness (GSS
Data)
FREQUENCY PERCENT VALID PERCENT
1. Very Happy 336 33.6 33.8
2. Pretty Happy 554 55.4 55.7
3. Not Too Happy 105 10.5 10.6
0. Not Available 5 0.5 MISSING
Total 1000 100 100
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Frequency Distribution of General Happiness

• REPORT Thirty-four percent of respondents report
  feeling very happy taken all things together,
  while 56 report feeling pretty happy, and 11
  not too happy.
• INTERPRET Thus, the majority of respondents feel
  pretty happy.

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Univariate Analysis, Continued

• Measures of Central Tendency place where the
  distribution of the variables values are fairly
  centered measures of central tendency tell us a
  little bit about the overall sample
• Mean average value
• Median the middle value half your values will
  be above it, half below it
• Mode the most frequently occurring value in the
  distribution

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Descriptive Statistics for Age (GSS Data)
N Min Max Mean Standard Deviation
Age of Respondent 998 18 89 44.9 18.03
REPORT The mean age for the sample is 45 years
old with a standard deviation of 18. Please
Note Mean is a measure of central tendency
standard deviation is a measure of dispersion
(together they are descriptive stats)
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Univariate Analysis, Continued

• Measures of Variation/Dispersion
• Range highest value in a distribution minus the
  lowest value (minimum-maximum)
• Variance average squared deviation of each case
  from the mean (used to calculate st. deviation)
• Standard Deviation the square root of the
  variance tells you how much dispersion (or
  spread) there is in the variable for your sample

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Levels of Measurement -gt Univariate Analysis

• Nominal Level
• Mode
• Frequency Table
• Ordinal Level
• Mode
• Mean
• Frequency Table
• Interval Level
• Median
• Mean
• Frequency Table
• Ratio Level
• Mean
• Sometimes researchers calculate the mean of
  ordinal and interval level variables, but we
  should do so with caution

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Bivariate Analysis

• analysis of the relationship between two variables

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Bivariate Analysis

• Cross-tabulations shows you the distribution of
  one variable for each category of another
  variable (IV in rows, DV in columns) looking to
  see the overlap in the relationship between the
  two variables
• Existence do the distributions of the
  attributes in the DV vary at all across
  categories of the IV?
• Strength how much do the distributions vary?
  are they large?
• Direction (positive or negative) only discussed
  when the IVs are ordinal, interval or ratio
  level do the values of the DV variable tend to
  increase with the values on the IV?
• Nature/Pattern are the changes fairly regular
  (just increasing or decreasing) OR do the
  percentages vary (curvilinear)?

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How to Read a Cross-tab

• Percentage Distributions are more useful than
  frequencies b/c can make comparison up and down
  categories of the IV
• Location of IV and DV
• IV is usually in the ROWS (increasing from top to
  bottom)
• DV is usually in the COLUMNS (increasing from L
  to R)
• Cell each box in the table is a cell
• Cell Frequency number of cases with 2
  attributes simultaneously

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How to Read a Cross-tab

• Totals

Dependent Variable
Independent Variable
100 100 100
Compare Up/Down Attributes of IV
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Cross-tab of Race and People Fair or Try to Take
Advantage (1972-96 General Social Survey Data)
1. Take Advantage 2. Fair 3. Depends Row Totals
1. White 32.1 62.9 5 100.0
2. Black 60.9 32.0 7.1 100.0
3. Other 45.0 48.2 6.8 100.0
Column Totals 36.2 58.5 5.3 100.0
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Cross-tab of Race and People Fair or Try to Take
Advantage

• Hypothesis I hypothesize that race will be
  associated with peoples views of others
  fairness, such that Whites will be more likely to
  think others are fair than Blacks and Other
  Races.
• REPORT Thirty-two percent of Whites in the
  sample said that people take advantage, while 61
  of Blacks and 45 of Other Races said people take
  advantage. Sixty-three percent of Whites versus
  32 of Blacks and 48 of Other Races said people
  tend to be fair. Only 5-7 of respondents from
  all three races said it depends.
• INTERPRET Whites tend to believe more so than
  Blacks and Other Races that people are fair.