Statistical Tools for Research ---SPSS (2)
Topic: Quantitative Data Analysis (Intermediate)
Date: April 14 & 15, 2003
Time: 6:00 - 8:30pm
Venue: B0415 & B0416
Facilitators: Dr. Zhang Wei-yuan (CRIDAL, OUHK)
Ms. Elaine Kwok (CRIDAL, OUHK)
This is the second session of workshops on quantitative data analysis using Statistical Package for the Social Science (SPSS) for Windows. This workshop will describe some basic statistical concepts and introduce techniques in One-Way ANOVA (Analysis of Variance), Reliability Analysis, Non-Parametric Techniques, and Multiple Response and Multiple Dichotomy analysis.
Recommended reading:
Norusis, M. J. (2000). SPSS10.0: Guide to Data Analysis, New Jersey: Prentice Hall.
Ferguson, G. A. & Takane, Y. (1989). Statistical Analysis in Psychology and Education, 6th ed,. New York: McGraw-Hill Publishing Company.
Mertens, D. M. (1998). Research Methods in Education & Psychology: Integrating Diversity with Quantitative & Qualitative Approaches, California: Sage Publications.
Wiersma, W. (2000). Research Methods in Education: An Introduction Research, 7th edn, MA, USA: Allyn & Bacon.
Lesson 5: To Run One-Way ANOVA (Analysis of Variance)
Comparing more than two population means
Example: If you use four different methods for teaching English, you want to compare average test scores for all four groups.
Independent variable and dependent variable
n Independent variable: a variable that affects (or is assumed to affect) the dependent variable under study and is included in the research design so that its effect can be determined.
n Dependent variable: a variable being affected or assumed to be affected by the independent variable.
Example 1: The effect of four teaching methods on reading scores on students.
n Independent variable: teaching methods
n Dependent variable: reading scores
Example 2: People’s average number of working hours are affected by their educational levels
n Independent variable: educational levels (less than high school; high school; junior college; bachelor; and graduate).
n Dependent variable: the average number of hours worked in a week
To obtain a one-way analysis of variance (ANOVA):
· You must indicate the variable whose mean you want to compare, and move it into “Dependent List”
· Select the variable whose values define the groups and move it into “Factor” box
· Click OK
Exercise:
>Open file “gssft”
>Click Analyze - Compare Means - One-way ANOVA
>Select the variable “hrs1” and move it into “Dependent List”
>Select the variable “degree” and move it into “Factor box”.
>Click “OK”
Bonferroni Multiple Comparison Test
Many multiple comparison procedures are available. One of the simplest is the Bonferroni procedure.
<click Analysis-Compare Means-One-way ANOVA
>Select the variable “hrs1” and move it into “Dependent List”
>Select the variable “degree” and move it into “Factor box”
>click “Post Hoc” and tick Bonferroni
>Set significance level at 0.05 or 0.01
>click “Continue” and then “OK”
The difference in hours worked between the two groups is shown in the column labeled Mean Difference. Pairs of means that are significantly different form each other marked with an asterisk.
Results:
People with graduate degree work significantly longer than people with less than a high school education;
People with graduate degree work significantly longer than people with just a high school education.
Exercise
1. Repeating the sample above.
2. Use the “Gss.sav”data file:
· Is there a relationship between highest degree earned and number of hours of television viewed a day (variable “degree” & “tvhours”)?
· Dependent variable: the average number of hours of TV viewed a day
· Independent variable: educational levels (less than high school; high school; junior college; bachelor; & graduate).
Further Reading:
Norusis, M. J (2000) SPSS10.0: Guide to Data Analysis, New Jersey: Prentice Hall.
259 – 277.
Lesson 6: Reliability Analysis
· Reliability means consistency. It is the degree to which an instrument will give similar results for the same individuals at different times.
· Reliability can take on values of 0 to 1.0, inclusive.
Methods for checking Reliability:
Test-retest reliability
The calculation of test-retest reliability is straightforward. The same test is administrated on two occasions to the same individuals under the same conditions. This yields two scores for each person and the correlation between these two sets of scores is the test-retest reliability coefficient. If the test is reliable, there will be a high positive association between the scores.
· Exercise: The scores of 20 students in language proficiency test and retest
· Inputting the following data
Student / Test / Retest1 / 94 / 96
2 / 92 / 87
3 / 88 / 91
4 / 87 / 86
5 / 87 / 89
6 / 86 / 86
7 / 85 / 89
8 / 95 / 91
9 / 85 / 84
10 / 83 / 86
11 / 82 / 84
12 / 81 / 77
13 / 78 / 81
14 / 76 / 71
15 / 72 / 76
16 / 68 / 72
17 / 66 / 66
18 / 65 / 72
19 / 63 / 59
20 / 58 / 55
To conduct a reliability analysis
Analyze-Correlate– Bivariate – click “Pearson” and “Flag”
Move “Test” and “Retest” to “Variables”-click “OK”
Pearson Correlation Result: r = 0.947
Split half
Only need one administration. The test items are divided into two halves, with the items of the two halves matched on content and difficulty.
Exercise: Interest Inventory (RIASEC)
Five-point scale:
· very much like me 5
· somewhat like me 4
· neither like nor unlike me 3
· somewhat unlike me 2
· very much unlike me 1
Social type
1. Easy to talk with all kinds of people
2. Good at explaining things to others
3. Enjoying working as a neighbourhood organiser
4. Teach children easily
5. Teach adults easily
6. Help people who are upset or troubled
7. Good understanding of social relationships
8. Good at teaching others
9. Making people fell at ease
10. Better at working with people than things or ideas
Inputting the following data
It1 / It2 / It3 / It4 / It5 / It6 / It7 / It8 / It9 / It101 / 2 / 5 / 3 / 1 / 4 / 5 / 2 / 1 / 2 / 4
2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
3 / 2 / 2 / 2 / 1 / 2 / 1 / 2 / 1 / 2 / 2
4 / 1 / 2 / 1 / 1 / 1 / 4 / 2 / 1 / 1 / 2
5 / 2 / 5 / 2 / 2 / 2 / 3 / 2 / 1 / 2 / 2
6 / 1 / 1 / 1 / 2 / 2 / 2 / 3 / 1 / 1 / 1
7 / 2 / 3 / 2 / 1 / 3 / 2 / 3 / 1 / 2 / 3
8 / 1 / 4 / 1 / 5 / 1 / 1 / 2 / 1 / 1 / 1
9 / 3 / 2 / 2 / 4 / 2 / 2 / 3 / 1 / 2 / 2
10 / 1 / 1 / 1 / 1 / 1 / 2 / 1 / 1 / 1 / 3
To conduct a reliability analysis
Analyze – Scale – Reliability analysis
Move the variables (i.e. It1 to It10) into the “Items” box
>In “Model” box select “Split-half”
>Click “Statistics”-under the “Descriptive for”-click “Scale”& “Scale if item deleted”; and then under the “Inter-Item”-click “Correlations”
>Click “Continue” and then “OK”
Report:
Guttman Split-half = 0.6164
If deleting item “it4”, the Alpha will raise to 0.7860.
Cronbach alpha
Prof. Lee J. Cronbach, Stanford University.
Attitude scales
Five point Likert scale format
Strongly agree Agree Undecided Disagree Strongly disagree
(5) (4) (3) (2) (1)
e.g. Please circle the choice after each statement that indicates your opinion.
· Students can learn to become a scientist without losing their cultural values.
· Science alienates people from their traditional culture.
Exercise: Scale for Measuring Attitudes Towards Mathematics or Science.
Strongly agree / Agree / Undecided / Disagree / Strongly disagree1. I want to develop my mathematical (science) skills and study this subject more. / 5 / 4 / 3 / 2 / 1
2. Mathematics (science) is not a very interesting subject. / 5 / 4 / 3 / 2 / 1
3. Mathematics (science) is a very worthwhile and necessary subject. / 5 / 4 / 3 / 2 / 1
4. Mathematics (Science) makes me feel nervous and uncomfortable. / 5 / 4 / 3 / 2 / 1
5. I have usually enjoyed studying mathematics (science) in school. / 5 / 4 / 3 / 2 / 1
6. I don’t want to take any more mathematics (science) than I absolutely have to. / 5 / 4 / 3 / 2 / 1
7. Other subjects are more important to people than mathematics (science). / 5 / 4 / 3 / 2 / 1
8. I am very calm and unafraid when studying mathematics (Science). / 5 / 4 / 3 / 2 / 1
9. I have seldom liked studying mathematics (Science). / 5 / 4 / 3 / 2 / 1
10. I am interested in acquiring further knowledge of mathematics (science). / 5 / 4 / 3 / 2 / 1
Inputting the following data
S1 / S2 / S3 / S4 / S5 / S6 / S7 / S8 / S9 / S10Q1 / 4 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3
Q2 / 2 / 1 / 2 / 4 / 3 / 5 / 1 / 3 / 2 / 2
Q3 / 4 / 4 / 4 / 3 / 5 / 3 / 3 / 3 / 5 / 3
Q4 / 1 / 2 / 3 / 4 / 3 / 3 / 3 / 3 / 2 / 3
Q5 / 5 / 2 / 4 / 3 / 4 / 4 / 2 / 1 / 3 / 3
Q6 / 1 / 3 / 4 / 4 / 1 / 3 / 3 / 4 / 3 / 3
Q7 / 5 / 4 / 3 / 3 / 4 / 2 / 4 / 2 / 3 / 3
Q8 / 4 / 2 / 4 / 3 / 2 / 4 / 3 / 1 / 3 / 3
Q9 / 2 / 3 / 2 / 4 / 3 / 5 / 3 / 2 / 2 / 3
Q10 / 5 / 3 / 4 / 3 / 1 / 3 / 3 / 3 / 3 / 3
Positively worded items from the questionnaire: 1, 3, 5, 8, 10
Negatively worded items from the questionnaire: 2, 4, 6, 7, 9
· Recoding value
Recoding negatively worded items: 2, 4, 6, 7, 9
· Transform – Recode – into Same Variables – move variable(s) to be recoded into “Numeric variables”, i.e. 2, 4, 6, 7, 9
>Click Old and new variable- from “old value”-click “Value” and put 1; from “new value”-click “Value” and put 5
>click “Add”
>Repeat the same for value (old value 2=new value 4; old value 3=new value 3; old value 4=new value 2; old value 5=new value 1)
>Click “Continue”
>Click “OK”
Or Transform – Recode – into Different Variables –move variable(s) to be recoded into “Numeric variables-
>Click “Output Variable”
>Under “Name”-type in a new name for this variable
>Under “Label”-type in a new label for this variable
>Click “Change”
>Click Old and new variable- from “old value”-click “Value” and put 1; from “new value”-click “Value” and put 5
>click “Add”
>Repeat the same for value (old value 2=new value 4; old value 3=new value 3; old value 4=new value 2; old value 5=new value 1)
>Click “Continue”
>Click “OK”
· To conduct a reliability analysis
Analyze – Scale – Reliability Analysis – Move the variables (i.e. Q1 to Q10) into the “Items” box
>In “Model” box select “Alpha”
>Click “Statistics”-under the “Descriptive for”-click “Scale”& “Scale if item deleted”; and then under the “Inter-Item”-click “Correlations”
>Click “Continue” and then “OK”
Report:
· Cronbach Alpha Results: Alpha = 0.6572
· If deleting item 7, the Alpha will raise to 0.7904.
Lesson 7: Non-Parametric Techniques
For the most non-parametric analyses, assumptions about the shape of the population are not required. For that reason, they are often used when small sample sizes are involved.
Chi-square test for goodness of fit
(One-sample Chi-square test: only one variable)
Exercise:
A researcher is interested in the factors that are involved in course selection. A sample of 50 students is asked, “Which of the following factors is most important to you when selecting a course? Students must choose one and only one of the following alternatives.
1. Interest in course topic
2. Ease of passing the course
3. Instructor for the course
4. Time of day course is offered
The frequency distribution of responses for this sample is as follows:
Interest in topic / 26Ease of passing / 12
Course instructor / 7
Time of day / 5
· Inputting the following data
Factors (factor) / Frequency (freq)1 / 1 (Interest in topic) / 26
2 / 2 (Ease of passing) / 12
3 / 3 (Course instructor) / 7
4 / 4 (Time of day) / 5
>Go to tool bar “Data” - Weight Cases - move “Freq” into “Frequency Variable” box-click “OK”
>Analyze – Nonparametric Tests – Chi-square – move “Factor” into the “Test Variable List” box-click “OK”
· Results: P = 0.000 < 0.05
· Conclusion: some of the factors are more important than others in course selection.
Chi-square test for relatedness or independence (2 x 2 table)
Exercise:
Purpose: To determine whether or not the gender is an important factor in students’ course selection
Sample: 74 male students and 72 female students
Preference for course selecting
Male / FemaleScience / 46 / 26
Social science / 28 / 45
· Inputting the following data
Labels
· Gender: 1=male 2=female
· Preference of courses (pref): 1=science 2=social science