Data Analysis
Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved.
Slide 1
3. Amount of Data Determine amount of data needed to conduct study Data sources, time periods, and number of units sampled Involves sampling techniques
•Sampling  Aim of sampling is to equate unknown
characteristics that may influence variation and to preserve the representativeness of the sample
Two Classes of Sampling Techniques: 1. Non-probability Sampling 2. Probability Sampling
1. Non-probability Sampling  Common feature is that subjective judgments
are used to determine the population that are contained in the sample.
A. Convenience sampling Select cases based on their availability for the study
B. Judgmental sampling Select cases based on some purpose (Most similar\dissimilar, Typical or Critical cases)
C. Systematic Sampling Select cases based on some predefined criteria (Interval sampling)
Every 4th
Advantages of Non-probability sampling  Fast, low effort\cost methods
 Useful in exploratory research
2. Probability Sampling  Common feature is that each unit in the
population has a known, nonzero probability of being included in the sample
A.Simple Random Sample Each member of the study population has an equal probability of being selected
B. Stratified Random Sample Each member of a population is assigned to a group or stratum, then random sample is drawn from each stratum (ensures levels represented)
C. Proportional Random Sample Each member of a population is assigned to a sub-group, then representative sample is drawn from each group proportional to population
Advantages of Probability Sampling  Objective standards remove possibility of
unknown confounds  Intent to remove bias in selection process
4. Accuracy and Reliability of Data  Issues of data quality: validity, reliability and
utility of measurement  Reduction of error in measurement
5. Design Fit  Statistical Conclusion Validity
 Utility (Efficiency/Generality)
Scales of Measurement 1. Nominal or Categorical 2. Ordinal 3. Interval 4. Ratio
1. Nominal or Categorical Classification according to presence or absence of qualities No information provided on order or magnitude of differences Because nominal scales have no quantitative properties, data
consist of frequencies only – E.g., sex, race, religion, political party
Yes
No
45
76
37% Yes No 63%
2. Ordinal Classification according to degree of quality present Distinguish between ordered relationships between
classes or characteristics, but no information about the magnitude of difference – E.g., tall > normal > short first > second > third
3. Interval Addition of a meaningful unit of measure: equal size
interval Consistent and useful unit of measure allows the use of basic arithmetic functions (addition, subtraction, multiplication, division) – E.g., Fahrenheit scale, shoe size
20
February
15
March
20
April
25
May
30
June
35
July
40
August
45
September
40
October
35
November
30
December
25
January 7%
6%
February
4%
March
8%
6% 7%
10%
April May June
8%
Au gu st Se pt em be r O ct ob er No ve m be De r ce m be r
Ju ly
Ju ne
M
ay
11% Ap ril
Ja nu ar y Fe br ua ry M ar ch
50 45 40 35 30 25 20 15 10 5 0
January
July August
10% 12%
11%
September October November December
4. Ratio Addition of an absolute zero point to interval scale Zero implies total absence of the characteristic Ability to utilize ratio statements (2:1, 1:5) – E.g., Height and weight
Bar Graphs
Qualitative Data (Nominal\Ordinal) Width of the bars is constant Bars separated by constant distance Normally height of bar corresponds to frequency of category Concerns: • Orientation (horiz vs. vertical) • Grid lines • Axes & Tickmarks • Fill • Order
Figure 1. Prevalence of Eye Color 8
Frequency
6
Blue Brown Green Black
4 2 0
Eye Color
Elements needed: •Identification (Figure #) •Title •Labels\Headings Remember: Figure should read like a self-contained paragraph.
Quantitative Data (Interval\Ratio) Histogram (similar to Bar Graph)
• Okay to put breaks in axis where set of values omitted • Bar widths represent real limits • Therefore, touch • Keep bar widths constant
Figure 2. Scores of First Exam 15
Frequency
10 5 0
95-99
94-90
89-85
84-80
79-75
74-70
69-65
Test Scores
Elements needed: •Identification (Figure #) •Title •Labels\Headings
64-60
59-55
54-50
Quantitative Data (Interval\Ratio)  Frequency Polygon
• Values represented as points above interval
Figure 3. Scores of First Exam
Frequency
14 12 10 8 6 4 2 0 95-99
94-90
89-85
84-80
79-75
74-70
69-65
64-60
59-55
54-50
Test Scores
Elements needed: •Identification (Figure #) •Title •Labels\Headings Remember: Figure should read like a self-contained paragraph.
10%
Strongly Agree
17%
44%
Agree Disagree Strongly Disagree
29%
20 18 16 14 12 10 8 6 4 2 0
18
12 Series1 7 4
Strongly Agree
20
18
15 12
10
7
5
Series1
4
Agree
12
Disagree
7
Strongly Disagree
4
S1 Strongly Disagree
18
Disagree
Strongly Agree
Agree
Strongly Agree
0
20 18 16 14 12 10 8 6 4 2 0
Agree
Disagree
Strongly Disagree
18
12 Series1 7 4
Strongly Agree
Agree
Disagree Strongly Disagree