Types of tests & their function Flashcards
Correlation
To see if there’s a linear association between two continuous variables.
The extent that two variables are related to each other.
Is there a relationship between the two variables?
Hypothesis:
H0: r = 0
H1: r ≠ 0
Results:
Liking of Brand A was significantly positively correlated with average monthly spending on Brand A’s products (r=[Pearson Correlation], p-value).
Binomial test
Comparing one proportion against a specified value.
Hypothesis:
H0 = __ %
H1 ≠ __ %
Results:
A binomial test revealed that the percentage of students who saw at least one movie this month (%) was significantly higher than 50% (exact binomial test: p-value)
Chi-square test
To determine is there is a significant assocation between 2 categorical variables.
–> % of something for one group is compared to the % of the same thing of another group
Example: Based on our survey, 45% of junior HKU students are subscribing to Netflix and 55% of senior HKU students are subscribing to Netflix. Are senior students more likely to be subscribing to Netflix than junior students?
Example:
Year: Junior/ Senior
Subscribed to Netflix: Yes/ No
Is the difference between the likelihood of juniors and seniors subscribing to Netflix statistically significant?
Hypothesis:
x = probability (%) of (a group) having (done what the nominal variable is about)
y = probability (%) of (the other group) having (done what the nominal variable is about).
H0 (null hypothesis): x = y (probability of both groups having done the things is the same, no difference)
H1 (alternative hypothesis): x ≠ y (there is a difference between both groups)
Results:
A chi-square test revealed a significant association between gender (2 different groups) and the likelihood of purchasing a kitchen item from Japan Home Centre in the past six months (1 response/question). Female consumers were more likely to have made such purchases (54.1%) compared to male consumers (21.6%), Pearson χ2(1[df], N[# valid cases] = 74) = 8.27, p = .004.
One sample t-test
To see if a mean is significantly different (higher or lower) from a proposed mean.
Is the mean of what we’re looking for significantly higher or lower than the proposed mean?
u = population mean
H0: u = #
H1: u ≠ #
Results:
A one sample t-test revealed that the mean of overall satisfaction with Starbucks was significantly lower than the scale midpoint of 4 (t(149[df]]) = -2.42[t], p-value)
Independent sample t-test
1 response/ question from 2 different groups of people.
To see if there’s a difference between the mean of the question between both groups.
Example: Is the liking of Movie X different between female and male students?
Hypothesis:
H0: u(female) = u(male)
H1: u(female) ≠ u(male)
Results:
An independent sample t-test revealed that female students like movie X more (M, SD), than the male students (M, SD; t(df)=#, p-value)
Paired sample t-test
Seeing the difference between the 2 responses from the same group of people.
2 responses/questions from the same people.
Example: Is the tendency to like seeing movies at home different from the tendency to like seeing movies in theaters?
Hypothesis:
H0: ud [difference of the means] = 0
H1: ud ≠ 0 –> there is a difference between the mean of both responses.
Result:
A paired t-test revealed that the tendency to like watching movies at home (M[mean], SD) did not significantly differ from the tendency to like watching movies in theaters (M, SD, t(df)=#, p-value)
One-way analysis of variance (ANOVA)
Determines whether there are any differences between the means of three or more independent groups
Hypothesis:
H0 = u(group 1) = u(group 2) = u(group 3)
H1: atleast one group mean differs
F-stat important (bigger the better = one of the means is different from the others): Examines the ratio of between-group variance to within-group variance.
Results:
ANOVA: The one-way ANOVA comparing satisfaction with Starbucks on HKU campus across students in different years was significant (F(df between groups, df within groups)=#, p-value)
Post Hoc Tests: Multiple Comparisons: The results revealed that group 1 (M, SD), liked Starbucks significantly more than group 2 (M, SD, p-value), group 3 (M, SD) liked Starbucks marginally significantly more than group 2 (p-value), the extend to which students liked Starbucks did not differ between group 2 and 4 (M, SD, p-value).
Simple linear regression
Does X effect Y?
Y = B0 + B1x1 + e
Hypothesis:
H0: B1 = 0
H1: B1 ≠ 0
B1 is significant if the p-value is significant.
Multiple linear regression
Seeing how various factors (independent variables) affect Y.
Factor analysis
Identifies underlying relationships between variables to group variables together (groups related variables and uncovers patterns)
Each factors represents a combination of the original variables.
Cluster analysis
Cluster analysis aims to identify natural groupings within a dataset. By analyzing the similarities and differences among data points, the technique helps to categorize them into clusters, where items in the same cluster are more similar to each other than to those in other clusters.
Multidimensional scaling:
A statistical technique used in marketing research to visualize the similarities or dissimilarities between a set of items, brands, or products. It helps researchers understand how consumers perceive various entities in a multi-dimensional space.
Descriptive/ survey research:
Used to figure out the characteristics of consumers and/ or markets.
- Who one’s customers are.
- What their beliefs, attitudes and opinions are.
- Where they shop.
Survey
Descriptive/ survey research: Cross-sectional
One sample, one point in time
Descriptive/ survey research: Longitudinal
One sample, different points in time
