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:? Footer text 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:? Footer text Page 11 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