This document provides an overview of quantitative data analysis techniques including data verification, frequency distributions, measures of central tendency and variability, and distributions. Key points: - Data should be verified to ensure accuracy through techniques like ordering, frequency distributions, and scatterplots to identify outliers. - Descriptive statistics like the mode, median, and mean are used to describe variables. The standard deviation measures variability. - Distributions can be normal, positively skewed, or negatively skewed depending on where values are clustered. The normal distribution is symmetric and bell-shaped.

1. 1
Chapter 11: Descriptions of
Quantitative Data
Science is facts; just as houses are made of stones, so is science made of
facts; but a pile of stones is not a house and a collection of facts is not
necessarily science.
-Henri Poincare, French mathematician & physicist (1854 - 1912)

2. 2
Data Analysis
 Telling your story about the data, whether
quantitative or qualitative.
 What is typical or common in the data.
 All respondents are teenagers.
 Most have improved after an intervention.
 What is the extent of difference or variation?
 Income ranges from $2,300 to $56,000.
 Attitudes differ by income.

3. 3
Data Verification
 Garbage in, Garbage out
Ensure that data have been entered correctly.
 Data ordering
 Use array: order data in ascending or
descending order by column and visually inspect
data for possible errors.
 Use frequency distribution for values of each
variable’s attributes.

4. Frequency Distribution
 Nominal Level
 Missing data (male = 1; female = 2; missing =9)
 Ordinal Level
 Interval and Ratio Level
 May not be appropriate
4
Frequency Percent Valid Percent Cumulative Percent
Strongly Disagree 18 9.5 9.5 9.5
Disagree 25 13.2 13.2 22.7
Neither 51 26.8 26.8 49.5
Agree 62 32.6 32.6 82.1
Strongly Agree 34 17.9 17.9 100.0
Total 190 100.0 100.0

5. 5
Data Verification
 Scatterplots are used to identify outliers.
 Then need to determine whether error is data
entry or data recording error.
0
5
10
15
20
25
30
0 250
x
Age
AGE
Scatterplot of Age Variable

6. 6
Recoding data
 Collapse or create categories.
 When some attributes have only a few responses.
 When it makes theoretical sense.
 E.g., collapse Asian/Pacific Islander with “Other.”
What do you consider yourself to be?
269 50.8 54.0 54.0
99 18.7 19.9 73.9
52 9.8 10.4 84.3
21 4.0 4.2 88.6
6 1.1 1.2 89.8
51 9.6 10.2 100.0
498 94.0 100.0
32 6.0
530 100.0
White, Non-Hispanic
African American
American Indian
Hispanic, Latino, Spanish
Asian or Pacific Islander
Other
Total
Valid
SystemMissing
Total
Frequency Percent Valid Percent
Cumulative
Percent

7. 7
Quantitative Data
 Descriptive statistics – summary measures
 Univariate Analysis: Describing one variable at a
time.
 Measures of Central Tendency
 Mode: The most frequent value.
 What was the most frequently visited domestic violence
shelter in the city?
 Unimodal – a distribution with one mode.
 Bimodal – when two values are most frequently reported.
 Multimodal – when more than two values are most
frequently reported.

8. 8
Quantitative Data (cont’d.)
 Median – For interval or ratio level data.
 The value that divides the distribution in half.
 50% of scores are on each side of the median.
 If even number of values, the median is the average of
the two most central values
 Useful if extreme scores impact the mean.
 e.g., income or age.
 Mean – For interval or ratio level data
 The average.
 The sum of the values divided by the number
of values.
 1,2,2,1,4,2,1,3,2,1 = 19/10 = 1.9

9. 9
Measures of Variability
 Minimum – lowest value
 Maximum – highest value
 Range – (highest value – lowest value) +1
 Standard Deviation (SD)
 A statistical measure of the amount by which a
set of values differs from the mean.
 Used to compare the variability of distributions.
 The greater the value the greater the variation
 Used in statistical analysis.
 Used to interpret scores in the normal distribution.
 
N
xX
SD
 

2

10. 10
The Normal Distribution
 Properties – Bell shaped curve.
 Symmetric, unimodal, with a mean of 0.
 50% of data fall on either side of the mean.
 68.26% fall within one SD; 95% within 2 SD.
Life skills posttest
100.0
95.0
90.0
85.0
80.0
75.0
70.0
65.0
60.0
55.0
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
40
30
20
10
0
Std. Dev = 14.91
Mean = 64.1
N = 187.00
Scores approximate Normal

11. 11
Skewed Distributions
 The distribution is not symmetrical when plotted.
 Positively skewed – scores cluster to the left side of curve
 Longer tail to the right
 Negatively skewed – scores cluster to the right side
 Longer tail to the left
day s in care
4200.0
4000.0
3800.0
3600.0
3400.0
3200.0
3000.0
2800.0
2600.0
2400.0
2200.0
2000.0
1800.0
1600.0
1400.0
1200.0
1000.0
14
12
10
8
6
4
2
0
Std. Dev = 761.50
Mean = 2113.8
N = 83.00
Grade Point Av erage
4.00
3.75
3.50
3.25
3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
60
50
40
30
20
10
0
Std. Dev = .69
Mean = 2.94
N = 190.00
Positive skew Negative Skew