Section B.3: Hypothesis testing (2)

Question 1

T-test

Answer 1

A t-test is a parametric test used to determine statistical differences between the means of two independent groups.

Question 2

What is a paired t-test?

Answer 2

A paired samples t-test is used to compare the means of two related (non-independent) groups. Such as a group of people before and after administration of a drug.

Question 3

Analysis of Variance (ANOVA)

Answer 3

Analysis of variance is a statistical method used to analyse the differences between two or more group means and determine whether those differences are significant.

Question 4

Types of ANOVA (3)

Answer 4

One-way ANOVA: Used to compare one independent variable with three or more levels with the mean of each level

Two-way ANOVA: Used to compare two independent variables effect and interaction with the dependent variable

N-way ANOVA: Used when there are more than two independent variables

Question 5

Outputs from ANOVA testing (4)

Answer 5

F-statistic: Measures the ratio of the between-group variance and within-group variance

p-value: Determines whether the f-statistic is statistically significant

mean square: the sum of squares divided by the degrees of freedom

effect size: measures the magnitude of the difference between group means

Question 6

Applications of ANOVA testing (3)

Answer 6

Medical research: Compare the effectiveness of treatments for a disease

Market research: Compare the mean ratings of products across demographic groups

Question 7

Advantages of ANOVA testing (3)

Answer 7

1. It can handle multiple groups simultaneously, making it useful for analysing complex datasets
2. It provides information about the significance of the differences between the means of groups
3. It can be used to detect interactions between multiple independent variable

Question 8

Limitations of ANOVA testing

Answer 8

1. It assumes normality and equal variances between groups
2. It cannot determine causality
3. It is sensitive to outliers

Question 9

Multivariate Analysis of Variance (MANOVA)

Answer 9

Multivariate Analysis of Variance (MANOVA) is a statistical method used to analyse the differences between group means of two or more dependent variables simultaneously

Question 10

Outputs of MANOVA testing (4)

Answer 10

Wilks’ lambda - Measures the extent to which the dependent variables differ between groups
F-statistic - Measures the ratio of the between-group and within-group variance-covariance matrix
p-value - determines if the f-statistic is statistically significant
Effect size - measures the magnitude of difference between the group means of the dependent variables

Question 11

Advantages of MANOVA testing (3)

Answer 11

1. It can analyse multiple dependent variables simultaneously, making it useful for analysing complex datasets
2. It provides more information than ANOVA as it can test for the interaction between the independent variables
3. It can handle unbalanced data, where the number of observations for each group is not equal

Question 12

Regression analysis

Answer 12

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It aims to determine how the independent variables affect the dependent variable.

Question 13

Applications for Regression analysis (3)

Answer 13

Regression analysis is used for:

1. Economic forecasting - Multivariate regression analysis is used to forecast economic variables such as inflation and GDP
2. Marketing - It can be used to determine the factors that influence consumer behaviours and decisions
3. Climate modelling - It is used to model the relationship between climate variables like temperature and rainfall

Question 14

Advantages of Regression analysis (3)

Answer 14

Can handle multiple predictors, gives info about the strength of the relationship, can predict outcomes

1. It can handle multiple predictors making it useful for modelling complex relationships between variables
2. It provides information about the strength of the relationship
3. It can be used to predict outcomes based on the values of the independent variables

Question 15

Limitations of Regression analysis (3)

Answer 15

1. It requires a large sample size to produce reliable results
2. It assumes linearity between the independent variables and the dependent variables
3. It is susceptible to multicollinearity - which occurs when the independent variables are highly correlated with each other

Question 16

Chi-squared analysis

Answer 16

Chi-squared analysis is a statistical method used to analyse categorical data. It involves comparing the observed frequencies of categorical data with the expected frequencies to determine if there is a significant association between the variables

Question 17

If the chi-squared statistic is greater than the critical value, is there a significant assocation? (T/F)

chi-sq > critical value = Reject H0, It is significant

Answer 17

TRUE

Question 18

Chi-squared analysis applications

Answer 18

Market research - Compare customer demographics and product preferences

Genetics - Determine association between genetic traits and disease susceptibility

Question 19

Advantages of Chi-squared analysis (3)

Answer 19

1. Easy to calculate and interpret - It does not require complex mathematical calculations
2. It can handle large sample sizes
3. It can be used with categorical data

Question 20

Limitations of chi-squared analysis (3)

Answer 20

1. It cannot determine causality between variables (cause and effect of associations that are seen)
2. It is limited to discrete categorical data
3. It is sensitive to small sample sizes which can affect the accuracy of results