The UK’s European university
Week 4: Quantitative
Research Methodology
Marketing Research
Yu-Lun Liu
Categorical Variable
Chi-square test
(Dependent Variable)
Discriminant analysis
Logistic Regression
Continuous Variable
Categorical Variable
(Independent Variable)
(Independent Variable)
Independent-samples
t-test
Paired-sample t-test
One-way ANOVA
Simple/Multiple Linear
Regression Analysis
Continuous Variable
(Dependent Variable)
Chi-Square
2
(χ )
Test
Two Categorical variables
卡方檢定：兩個類別變數
Chi-Square Test Statistic
a statistical method assessing the goodness of fit between a set of observed values and
those expected theoretically. It is used to test the relationship between two categorical
variables
The Chi-square test statistic is:
( fo  fe )
  
fe
all cells
2
2
• where:
fo = observed frequency in a particular cell 觀察到的次數
fe = expected frequency in a particular cell if H0 is true 預期的次
數
degree of freedom for 2 = (columns-1)(rows-1) 自由度為(行-1)*(列-1)
 2 for the 2 x 2 case has 1 degree of freedom (2-1)*(2-1) = 1
(Assumed: each cell in the contingency table has expected frequency of at least 5)
(Theoretical) Expected Cell Frequencies
• Expected cell frequencies:
row total  column total
fe 
n
Where:
row total = sum of all frequencies in the row
column total = sum of all frequencies in the column
n = total sample
• VARIABLE 1: Stage 1: 一開始的答案 (Categorical)
• VARIABLE 2: Stage 2: 跟組員討論後的結果 (Categorical)
• VARIABLE 3: GroupAorB:
A group – 答對加分組;
B group: 答錯扣分組(Categorical)
• VARIABLE 4: Programme: 1 – Masters（碩士）, 2 – undergraduate（
大學部）, 3 – EMBA+PMBA（進修部） (Categorical)
• VARIABLE 5: Changed answer: 1 – changed; 2 – remain the same
(Categorical)
Question: Whether people choose to (or not to) change
answer
when
under
different
conditions
(punishment/reward)? 是否人們會在不同的獎懲情況
下決定要不要改變自己原本的選擇（答案）？
H0: The condition (punishment/reward) will not affect
people’s intention to change their decision 獎懲情境不
會影響人們的決定
=
H1: The condition (punishment/reward) will affect
people’s intention to change their decision 獎懲情境會
影響人們的決定
≠
Hypothesis testing (two-sided)
Chi-square test
Under the
punishment condition
懲罰組
Changed response
Observed frequenc觀察次數:?
Under the
reward condition
獎勵組
Observed frequency:?
改變了答案
Remain the same
沒有改變答案
Expected frequenc理論預期次數:?
Expected frequency:?
Observed frequency:?
Observed frequency:?
Expected frequency:?
Expected frequency:?
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Page 9
Using SPSS to find the answer
Chi-square test
Under the
punishment condition
懲罰組
Changed response
Observed frequenc觀察次數:?
Under the
reward condition
獎勵組
Observed frequency:?
改變了答案
Remain the same
沒有改變答案
Expected frequenc理論預期次數:?
Expected frequency:?
Observed frequency:?
Observed frequency:?
Expected frequency:?
Expected frequency:?
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How to report your findings
• χ2 (degrees of freedom, N = sample size) = Chi-square statistic
value, p = p value.
• χ 2 (___, N = ___) = ___, p = (or < ) _____.
• A Chi-square test (χ 2 (1, N = 105) = 15.27, p < .01.) reveals that
people in a punishment condition are more likely to change their
decision and revise their previous choice. Therefore, H1 is supported.
• 卡方檢定顯示 (χ 2 (1, N = 105) = 15.27, p < .01.) 人們在
Now your turn:
Question: Compared to EMBA students, do Masters
students get affected by others more due to different
conditions (punishment/reward)?
相較於進修部同學，是否日間部碩士班同學受到獎
懲情境的影響較為顯著？
Make two-sided hypothesis for testing
(take 95% confidence level)
雙尾檢定假設
Question: Compare to EMBA students, do Masters
students get affected by others more due to different
conditions (punishment/reward)?
H0: EMBA students and Masters students get affected by
others option equally相較於進修部同學，日間部碩
士班同學不會受到獎懲情境的影響較為顯著
H1: EMBA students and Masters students do not get
affected by others option equally相較於進修部同學，日
間部碩士班同學會受到獎懲情境的影響較為顯著
Hypothesis testing (two-sided)
=
≠
Using SPSS to find the answer