This document provides an overview of quantitative research methods and statistical analysis techniques. It discusses descriptive statistics such as frequencies, measures of central tendency, variability, and relationships. It also covers inferential statistics including t-tests, which are used to assess differences between two groups, and correlation, which examines relationships between two variables. Examples of conducting statistical tests in SPSS are provided.

1. Quantitative Research Methods
Lecture 5
1. Numerical descriptive techniques
2. Descriptive statistics in SPSS
3. Inferential statistics
4. T-test
5. Correlation

2. Review 2: 2. Types of statistics
• Descriptive statistics: methods of organizing,
summarizing, and presenting data in ways that
are useful, attractive, and informative to the
reader
Forms Techniques Examples
Numbers Numerical Mean, median, range,
Graphics Graphical Bar charts
Pie charts
Histograms
Line charts
Scatter Diagrams

3. Review 2: 2. Types of statistics
• Inferential statistics:
methods used to draw
conclusions about a
population based on
information provided by
a sample of the
population
Population
Sample
A1
A
Inferential statistics:
Generalizing results
to population A

4. Review 2: Types of research
• Descriptive:
▫ Provides accurate description of a phenomenon
▫ Statistics used: Frequency and Descriptive
▫ Drawback: Does not intent to explain why
• Explanatory:
▫ Identify underlying factors to the phenomenon.
E.g., Is media a factor influencing body-figure?
Is gender a factor? Is educational level a factor?
Is peer influence a factor?
▫ Statistics used: T-tests, ANOVA, MANOVA,
correlations, multiple regression etc.

5. Review 2: Types of research and
appropriate statistics
Descriptive Explanatory
Frequency,
Descriptives
T-test, ANOVA, MANOVA,
Correlation, Multiple Regression
Descriptive statistics Inferential statistics

6. Review 2: Descriptive statistics
Descriptive
statistics
Frequency Descriptive

7. Inferential
statistics
Differences
between groups
Relationships
between variables
T-test, ANOVA Correlation, Multiple Regression

8. Descriptive statistics
Descriptive
statistics
Frequency Descriptive
Count, Percentage Mean, Median, Mode
Range, Variance, SD, CV
Percentile, Linear Relationship
Nominal/Ordinal
Data
Interval/Ratio
Data

9. Review 2.6. Hands on: Graphical
Descriptive Techniques I
Graphical
Techniques
Objective Data type Ex
Frequency and
Relative Frequency
(Proportion)
Tables
Bar charts
Pie Chart
Describe a single
set of data
Nominal or
ordinal
P18 GSS2008
P24
Xm02-02
P27
Ex2.11 Bar
Ex2.12 Pie
Cross-classification
Table
Cluster bar chats
Describe the
relationship
between two
variables and
compare two ore
more sets of data
Nominal P32
Xm02-04
P37
ANES2008

10. Frequencies in Excel
• COUNTIF (range, criteria)
• No percentage
• Week 1 Assignment 2 GSS2008
• From Excel to SPSS

11. The “Frequencies” function in SPSS
Subject Value Subject Value
1 3 6 3
2 4 7 2
3 3 8 3
4 1 9 4
5 2 10 3
How many have chosen ‘1’ as their answer? ‘2’? ‘3’? ‘4’? ‘5’?

12. Frequency Table
Value Frequency Percent Cumulative
percent
1 1 10% 10%
2 2 20%
3
4
total 10 100%

13. The “Frequencies” function in SPSS
• For a small sample size, we can count…
• But how about a sample size of 1000?

14. “Frequencies” in SPSS
• To run frequencies procedure:
• Analyze
Descriptive statistics
Frequencies (highlight variables
and move them to the right
column)
OK

16. “Frequencies” in SPSS
• Frequency output
• Frequency: The number of times a number
appears in the data set
▫ E.g., The frequency of the value ‘1’ is 1
• Frequency distribution: The number of times
each different number in the set appears
▫ E.g., Value Frequency
1 1
2 2
3 5
4 2
5 0
Total 10

17. “Frequencies” in SPSS
• Percentage distribution: The presence of
each different number expressed as a
percent
▫ E.g., Value Percent
1 10%
2 20%
3 50%
4 20%
5 0
Total 100%

18. “Frequencies” in SPSS
• Cumulative distribution: A running total of the
counts or percentages
• It indicates the sum of the counts (%) of all
preceding numbers plus the present one
• E.g., Value Percent Cum. Percent.
1 10% 10%
2 20% 30%
3 50% 80%
4 20% 100%
5 0
Total 100%

19. “Frequencies” in SPSS
• Valid percentage: The valid percentages are
determined after any missing values are
removed
• Frequency output
• The most useful column
• This column tells us that of the 2024
respondents who gave a valid response, % of
white, %black, % other. (GSS2008)

20. Descriptive statistics
• Mean: the average of the set of numbers
• Standard deviation: An indication of how similar or
dissimilar the typical responses are to the mean
• Mode: the response that is mostly chosen (the number
that has the largest frequency)
• Minimum: the smallest value of the response that has
been chosen
• Maximum: the largest values of the response that has
been chosen
• Range: maximum - minimum

21. Numerical Descriptive Techniques
Measures Tech Objective Data Type e.g.
Measures of
Central Location
Mean Single data, not good
for small number of
extreme observation
Interval
Median Single data, relative
standing
Ordinal/
Interval
grade
Mode Single data Nominal/Ordi
nal/Interval
Measures of
Variability
Range
Variance
Standard
Deviation
Coefficient
of Variance
Single data
The size of variability
Interval P108/
112
P112:
4.8

22. Numerical Descriptive Techniques
Measures Tech Objective Data Type e.g.
Measures of
Relative Standing
and Box Plots
Percentile
Quartile:
Q1 first/lower
Q2 second
Q3 third/upper
Interquartile Range
Single data
Q3-Q1
Interval SAT
GMAT
Excel
P118
Formula

23. Box Plot: multiple
• Example P 122 4.15

24. Numerical Descriptive Techniques
Measures Tech Objective Data
Type
e.g.
Measures of
Linear
Relationship
Type
equation here.
Covariance σ/s
relationship
Two
interval
variables
P134
4.17
Coefficient of correlation r
Relationship+
magnitude
Two
interval
variables
Coefficient of determination r2 explains %
of variation
Two
interval
variables
Least squares line line Two
interval
variables

25. Formula for Mean
where is mean, xi is the value of i-th case, n is the sample size，
is to summarize the values from the first to n-th cases.
x
n
x
x
i

 ix

26. Same Mean but Different SDs
1= 2
x x
1x
2x
Which
Standard
Deviation is
larger? SD1
or SD2?

27. Interpreting the Standard Deviation
1. Empirical Rule:
• Mean and SD
• Shape of Histogram: Bell
shaped (P50-51)
• 68% within 1 SD of Mean
• 95% within 2 SD of Mean
• 99.7% within 3 SD of Mean
▫ E.g. P113, 4.9
2. Chebysheff’s Theorem: all
shapes of histogram

28. Descriptive statistics in SPSS
Mode Maximum Minimum Mean Std.
Deviation
i1
Range= maximum-
minimum

29. Formula of Standard Deviation
1
)( 2




n
xx
s
i
where is mean, xi is the value of i-th case, n is the sample size，
n is the total number of cases.
x

30. Standard Deviation
• SD: An indication of how dispersed (similar/
dissimilar) the typical responses are to the mean
• If SD is small, the distribution of the greatly
compressed
• If SD is large, the distribution is consequently
stretched out at both ends

31. “Descriptives” in SPSS
• To run descriptive procedure:
• Analyze
Descriptive statistics
Descriptives (highlight variables
and move them to the right
column)
Options (choose statistics)
OK
• GSS2008 data

32. Inferential
statistics
Differences
between groups
Relationships
between variables
T-test, ANOVA, MANOVA Correlation, Multiple Regression

33. Main Analysis
Hypothesis
Prediction of
relationship between
variables
Prediction of group
difference in some
variables
T-test, ANOVA,
MANOVA
Correlation,
Multiple regression

34. Statistical analyses
• Group differences between 2 groups:
▫ T-tests
• Group differences among 3 or more groups
▫ One-way ANOVA
 Scheffe post-hoc test
• Relationship between 2 variables
▫ Correlation
• Relationship among 3 or more variables
▫ Multiple regression

35. Hypotheses regarding group
difference
• The hypothesis language
• Group A will be more (or less) in (something)
than Group B
• “ It is hypothesized that females would be
more likely to shop online than woman.”
• “It is predicted that males would trust more
about online shopping than woman.”

36. Testing group difference
• Comparing 2 groups’ difference in some
variables
• We use Independent-samples t-test
Male group Female group
Subj.1 Subj. 1
2 2
3 3
4 4
• Note: t-tests can compare only 2 groups at a
time

37. Comparing males and females on
these variables
Degree of enjoyment on online shopping M > F

38. Variable Female Male
Variable A
Testing group difference

39. Testing group difference
• The concept of being “statistically significant”
Male group Female group
Mean =2. 42 Mean = 2.11
• Can we jump into the conclusion that males are
greater than females in variable A?
• Not yet…
• We have to find out whether the difference could
really be claimed ‘a difference’
• “Is the difference statistically-significant?”
• T-test takes into consideration the difference in
means and the sample size to determine whether it
is statistically significant

40. The concept of being “statistically-
significant”
• We could only claim a difference as a real
difference when statistics tell you so
• The concept of being “statistically-significant”
• The SPSS language: p<.05

41. Being “statistically- significant”
• Significant level: p<.05
• If p<.05 (significant)
• You could claim that the difference is a real
difference, because it is statistically-
significant.
• If p>.05 (non-significant)
• You couldn’t claim there is a difference

42. Being “statistically- significant”
• Significant level: p<.05
• The logic behind:
• Statistics is about probability
• What does ‘p’ stand for
• p= probability of making an error in the
calculation leading to a conclusion that there
is a significant difference when in fact there
is not
• Type 1 error: Making a false claim that there
is a real difference between 2 groups when
there is indeed none
• When this probability is smaller than 5 out
of 100 acceptable

43. Being “statistically- significant”
• Type 1 error: Making a false claim that there
is a real difference between 2 groups when
there is indeed none
• When this probability is smaller than 5 out
of 100 acceptable
• p<.05 = probability of committing this Type
1 error is less than 5/100
• Over 95% of the time when you make the
claim that there is a difference between the
groups in certain aspects, you are correct
• p> .05 not acceptable, no real difference
between 2 groups.

44. Running T-tests
• Steps for running a t-test:
• Analyze
Compare means
Independent-sample T-test
Grouping variables
Define (which two
groups)
Testing variables

45. Running T-tests
• Task: Perform t-tests to see if there is any gender
difference in:
▫ (1) Degree of enjoyment on online shopping?
▫ (2) Degree of trust having friends through the
Internet?
▫ (3) Degree of parents’ monitoring on
teenager’s access through the Internet?
▫ (4) Degree of benefits from parents
involvement on teenager’s access through the
internet.
▫ (5) Degree of viewing oneself as an Internet
fanatic

46. Interpreting T-test results
• T-test output
• 1) Look at the means of the 2 groups (To
see which group has a higher mean)
• 2) Look at ‘Levene’s test of equality of
variance’:
• If non-significant> no significant different
in the variance> equal variance> rely on
the top row

47. Interpreting T-test results
• T-test output
• Step 1: The output from the t-test procedure
is segmented by two parts: variables and
types of information.
• Step 2: For each dependent variable, SPSS
reports descriptive statistics in the first part.
Look at the means of the 2 groups (To see
which group has a higher mean than the
other in a variable)
• Step 3: To see if there is significant
difference. We need to make reference to
part 2:

48. Interpreting T-test results
• Step 4: First look at “Levene’s test for
equality of variances”. It will help you
determine which t-test value to use. Note: It
doesn’t tell you whether the 2 groups are
statistically different.
▫ If “Levene’s test for equality of variances” is not
significant (the variances are not too different),
then use ‘equal variances assumed’ that is, look
at the 1st row and neglect the 2nd row
▫ If “Levene’s test for equality of variances” is
significant, then use ‘equal variances not
assumed’ that is, look at the 2nd row and neglect
1st row

49. • If p>.05 non significant the sample variance
does not differ variance is equal equal
variances assumed read the 1st row
• If p<.05 significant the sample variance
differs variance is not equal equal variances
not assumed read the 2nd row

50. Interpreting T-test results
• Step 5: Look at these figures: Mean-
difference, t value, and significance. This is
where the important information lies.
• Look at the “significance level”
• If p<.05
• There is a significant difference between the
2 groups
• If p>.05
• The 2 groups are not different in a particular
variable
• Run t-tests and complete the table

51. Reporting T-test results
• In reporting significant results:
• “The means for the Chinese-Canadian females
and Chinese-Canadian males in Maintenance
of Chinese culture were M=5.50 (SD =.98) and
M = 4.33 (SD =.97) respectively. T-test showed
that the Chinese-Canadian female subjects
scored significantly higher than their male
counterparts in the variable of Maintenance of
Chinese culture , t(99)= -3.01, p<.05.”
• You need to report the means, SDs, degree of
freedom, t-value, and significance.

52. Reporting T-test results
• In reporting non-significant results
• T-test showed no significant difference
between the Chinese-Canadian female
and male subjects i shyness, t(94)= .12,
n.s.
• *t(df)= t-value, significance level
• Units for significance level:
• p<.05, p<.01, or p<.001

53. Correlation
Variable A Variable B

54. Correlation
Social media use Less time with Family

55. Testing relationship between 2
variables
• Examining relationship between 2
variables
• Correlation
• The hypothesis language:
• “It is hypothesized that frequency of online
shopping is positively correlated with trust
towards online shopping.”
• “It is hypothesized that time of Internet
surfing is positively correlated with trust
towards friendship through internet.”
• Tutorial session: correlations

56. Running correlations
• Steps for correlation:
• Analyze
Correlate
Bi-variate (i.e., examining 2
variables at a time)
Variables (select the var. you
want to examine)
Pearson’s product
moment
correlation
Options> Means
and SD Missing
values (pairwise)

57. Interpreting correlation results
• Step 1: Significance level
• Step 2: Positive or negative? (direction of the
relationship)
• Step 3: Coefficients from –1.00 to +1.00
(magnitudes of the relationship)

58. Reporting correlation results
• For significant finding:
• “Correlation results showed that Westernization
was significantly and negatively correlated with
adolescents’ self-reported depression, r(110)= -
.49, p<.05. Hypothesis 1 was confirmed.

59. Reporting correlation results
• For non-significant findings. E.g.:
• “Results showed that no significant
correlation was found between
maintenance of Chinese culture and
self-reported depression, r(117)= .04,
n.s. Hypothesis 2 was disconfirmed.