Quantitative Research Method
Department of Applied Foreign Languages
謝育芬
Unit 4
Inferential Statistics:
T-test
Reference: 量化研究與統計分析（五版）（2010）。第七章。
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Types of Statistical Methods
Statistical
Methods
Descriptive Statistics Inferential Statistics
(to describe the (to make inferences about
characteristics of a sample) a population based on a
sample)
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Contents
The fundamentals of t-test
Performing t-test analysis using SPSS
Interpreting the data reports generated by SPSS
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T-test: Purpose
To test whether there is a significant difference
between the means of two sets of data.
e.g.,
male vs. female
pre-test score vs. post-test score
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T-test: Assumptions
Dependent variables are interval or ratio.
The population from which samples are drawn is
normally distributed.
Two sets of data have equal variance (homogeneity
of variance).
The t-statistic is robust (it is reasonably reliable even
if assumptions are not fully met).
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T-test: Types
Independent-samples T-test（獨立樣本）
Comparing means of 2 different groups.
Paired-samples T-test（相依樣本）
Comparing means of the same group in 2 different
conditions.
Only comparing 2 sets of data.
More than 3 sets of data -> use ANOVA.
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T-test: null hypothesis (H0)
There is NO significant difference between two sets
of data.
p (sig.) (α) < .05 reject H0
There is a significant difference between the means
of two sets of data.
(p : level of significance)
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T-test: two-tails vs. one-tail
Two-tails: to test the difference between two sets of
data in both directions (greater than AND less than).
One-tail: to test the difference between two sets of
data in only one direction (greater than OR less than).
The choice of two-tails or one-tail T-test depends on
the research question.
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Independent-samples T-test
To test if there is a statistically significant difference
in the means for 2 groups.
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Performing T-test: Independent-samples (1)
Analyze →
Compare Means →
Independent-Samples T-test
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Performing T-test: Independent-samples (2)
Test Variables: select Dependent Variable
e.g., post-test score
Grouping Variable: select Independent Variable
e.g., method
Define Groups: e.g., intervention=1, no intervention=0
Continue OK
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Data Output: Independent-samples T-test (1)
Descriptive Statistics
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Data Output: Independent-samples T-test (2)
Inferential Statistics
p=1.00 (> 0.05), so there is NO The two sets of data are
significant difference in the significantly different.
variances of the two sets of data. t = 2.28, p = .04
The equal variance assumption of
t-statistic is NOT violated.
變異數＝標準差的平方（所有資料到平均數的平均距離） 16
Variance
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Data Report: Independent-samples T-test
Report must include:
1) statistical method
2) statistical results
mean, standard deviation (SD)
t-value (positive or negative)
p-value (< .05 means “there is a significant difference
between two sets of data”. The smaller the p-value,
the larger the significance)
**All values are reported to two decimal digits.**
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Data Report: Independent-samples T-test
Example:
The study investigated the effect of xxx method on
students’ test scores. An independent-samples T-test
showed that there was a significant difference
between the post-test scores of the experimental class
and the control class (t =__, p< .05). The experimental
class (Mean=___, SD=___) received higher scores than
the control class (Mean=___, SD=___) .
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Paired-samples T-test
To test if there is a statistically significant difference
in the means of 1 group in 2 different conditions
e.g., pre-/post-test scores of Class A
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Performing T-test: Paired-samples (1)
Analyze →
Compare Means →
Paired-Samples T-test
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Performing T-test: Paired-samples (2)
Paired Variables: select the two variables to be
compared
e.g., pre-test score & post-test score
OK
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Data Output: Paired-samples T-test (1)
Descriptive Statistics
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Data Output: Paired-samples T-test (2)
Inferential Statistics
The two sets of data are
significantly different.
t = -3.47, p = .01
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Data Report: Paired-samples T-test
Report must include:
1) statistical method
2) statistical results
mean, standard deviation (SD)
t-value (positive or negative)
p-value (< .05 means “there is a significant difference
between two sets of data”. The smaller the p-value,
the larger the significance)
**All values are reported to two decimal digits.**
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Data Report: Paired-samples T-test
Example:
The study investigated the effect of xxx method on
students’ test scores. A paired-samples T-test showed
that there was a significant difference between the
pre-test scores and the post-test scores of the
experimental class (t =__, p< .05). The post-test scores
(Mean=___, SD=___) were higher than the pre-test
scores (Mean=___, SD=___).
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p-value
When t gets larger, p becomes smaller (difference
between two data sets is more significant).
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Exercise 1
A research study examined the differences between older
and younger adults on perceived life satisfaction. A pilot
study was conducted to examine this hypothesis. 20 older
adults (over the age of 70) and 20 younger adults (between
20 and 30) were give a life satisfaction test. Scores on the
measure range from 0 to 60 with high scores indicative of
high life satisfaction; low scores indicative of low life
satisfaction.
What statistical method should be used?
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Exercise 1
Data set
1=old group
2=young group
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Exercise 1
Compute the descriptive statistics (mean & SD) for the older
and the younger groups.
What would be the null hypothesis in this study?
H0 = There is no significant difference between older and
younger adults on life satisfaction.
Do the older and the younger groups differ in life satisfaction?
Older adults have significantly higher life satisfaction than
younger adults (t = 4.257, p < .001).
[independent-samples t-test]
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Exercise 2
To observe the effectiveness of a medication in reducing
blood pressure, an experiment was conducted in which
researchers collected data from a random sample of
individuals who had high blood pressure. The diastolic blood
pressure of these individuals was recorded, after which they
were placed on the medication. One month later, their
diastolic pressure was recorded again.
What statistical method should be used?
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Exercise 2
Data set
BP=Blood Pressure
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Exercise 2
Compute the descriptive statistics (mean & SD) for the
“BaselineBP” and the “NewBP” groups.
Was the medication effective in reducing blood pressure?
The average BP was significantly lower after the medication
than before (t=10.88, p= .000).
[paired-samples t-test]
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