Types of statistical tools

1. Measures of Central Tendency:

• Type of Problem: N/A

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variable

2. Measures of Variability:

• Type of Problem: N/A

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variable

3. t Test for Independent Samples:

• Type of Problem: Comparison of means between two independent groups

• Level of Measurement: Interval or ratio

• Number of Sample: Two independent samples

• Type of Sample: Random or independent

• Parametric Distribution Assumption: Normally distributed populations

4. t Test for Related/Dependent Samples:

• Type of Problem: Comparison of means for related samples

• Level of Measurement: Interval or ratio

• Number of Sample: Paired samples (two-sample)

• Type of Sample: Matched pairs or repeated measures (correlated)

• Parametric Distribution Assumption: Normally distributed population of differences (or sufficiently large sample size for the Central Limit Theorem to apply)

5. One-Way Analysis of Variance (ANOVA) F Test:

• Type of Problem: Comparison of means among three or more independent groups

• Level of Measurement: Interval or ratio

• Number of Sample: Three or more independent samples

• Type of Sample: Random or independent

• Parametric Distribution Assumption: Normally distributed populations within each group

6. Two-Way ANOVA F Test:

• Type of Problem: Comparison of means considering two independent variables

• Level of Measurement: Interval or ratio

• Number of Sample: Multiple samples in each combination of independent variables

• Type of Sample: Random or independent

• Parametric Distribution Assumption: Normally distributed populations within each combination of independent variables

7. F-Test for Repeated Treatment/Dependent Samples:

• Type of Problem: Comparison of means for repeated measures under different conditions

• Level of Measurement: Interval or ratio

• Number of Sample: Two or more related samples

• Type of Sample: Matched pairs or repeated measures

• Parametric Distribution Assumption: Normally distributed population of differences (or sufficiently large sample size for the Central Limit Theorem to apply)

8. Analysis of Covariance:

• Type of Problem: Comparison of means adjusting for a covariate

• Level of Measurement: Interval or ratio

• Number of Sample: Two or more independent samples

• Type of Sample: Random or independent

• Parametric Distribution Assumption: Normally distributed populations within each group for the covariate

9. Chi-square Test of Independence:

• Type of Problem: Association between two categorical variables

• Level of Measurement: Nominal

• Number of Sample: Two categorical variables

• Type of Sample: Random or independent

• Parametric Distribution Assumption: N/A (non-parametric test)

10. McNemar's Test:

• Type of Problem: Comparison of proportions in a 2x2 table

• Level of Measurement: Nominal

• Number of Sample: Two related samples

• Type of Sample: Matched pairs or repeated measures

• Parametric Distribution Assumption: N/A (non-parametric test)

11. Fisher's Exact Test:

• Type of Problem: Comparison of proportions in a 2x2 table (small sample sizes)

• Level of Measurement: Nominal

• Number of Sample: Two independent samples

• Type of Sample: Random or independent

• Parametric Distribution Assumption: N/A (non-parametric test)

12. Pearson Product Moment Correlation Coefficient:

• Type of Problem: Relationship between two continuous variables

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: Bivariate normality (normal distribution of the variables and their joint distribution)

13. Multiple Correlation:

• Type of Problem: Relationship between one continuous variable and two or more continuous variables

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: Multivariate normality (normal distribution of the variables and their joint distribution)

14. Partial Correlation:

• Type of Problem: Relationship between two continuous variables while controlling for a third variable

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: Bivariate normality for each pair of variables involved in the partial correlation

15. Spearman Rank Order Correlation:

• Type of Problem: Relationship between two ordinal variables

• Level of Measurement: Ordinal

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

16. Kendall's Coefficient of Concordance:

• Type of Problem: Agreement among multiple raters or judges

• Level of Measurement: Ordinal

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

17. Phi Coefficient:

• Type of Problem: Association between two binary variables

• Level of Measurement: Nominal

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

18. Somer's D:

• Type of Problem: Association between two ordinal variables

• Level of Measurement: Ordinal

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

19. Risk Ratio:

• Type of Problem: Comparison of the risk of an event between two groups

• Level of Measurement: Nominal

• Number of Sample: Two independent samples

• Type of Sample: Random or independent

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

20. Regression Analysis:

• Type of Problem: Prediction of a dependent variable based on one or more independent variables

• Level of Measurement: Interval or ratio

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: Residuals (errors) are normally distributed

21. Item Analysis:

• Type of Problem: Assessment of the quality of individual test items

• Level of Measurement: Ordinal or interval

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

22. Cronbach's Alpha:

• Type of Problem: Assessment of internal consistency in a scale or test

• Level of Measurement: Ordinal or interval

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: No specific assumption about the distribution of the variables

23. Exploratory Factor Analysis:

• Type of Problem: Identification of underlying factors in a set of observed variables

• Level of Measurement: Ordinal or interval

• Number of Sample: Any

• Type of Sample: Any

• Parametric Distribution Assumption: Multivariate normality for the observed variables

Sample problems: Identify which statistical tool should be used

Problem 1:

A school district is implementing two different teaching methods, A and B, to improve students' standardized test scores in mathematics. You want to compare the average test scores of two independent groups of students, one taught with method A and the other with method B. The test scores are measured on an interval scale.

Question:

Which statistical tool would be most appropriate for comparing the mean test scores of students taught with method A and method B?

Problem 2:

You are conducting a study on the relationship between the number of hours students spend studying per week and their final exam scores in a statistics course. You collect data from 30 students, recording the hours studied and their corresponding final exam scores, both measured on an interval scale.

Question:

What statistical tool would you use to assess the strength and direction of the relationship between the number of hours studied and final exam scores?

Problem 3:

A researcher is investigating whether there is a significant difference in the mean scores among three different training programs designed to improve employees' productivity. The scores are obtained from three independent groups of employees, and the data are measured on an interval scale.

Question:

Which statistical test would be appropriate for comparing the mean scores of employees who underwent three different training programs?

Problem 4:

You are studying the relationship between gender and the preference for a popular soft drink brand. You collect data from a sample of 200 individuals, noting their gender (male/female) and soft drink brand preference (Brand X, Brand Y, or Brand Z).

Question:

Which statistical test should be used to determine if there is a significant association between gender and the preference for the soft drink brand?

Problem 5:

Three judges independently rate the performances of 20 contestants on a talent show on a scale from 1 to 10. You want to analyze the agreement among the judges' ratings.

Question:

Which statistical tool is suitable for analyzing the agreement among the three judges in rating the performances?

Problem 6:

You work for a marketing research firm and want to predict the final sales of a new product based on advertising expenditure (in dollars) and the number of social media mentions. You collect data from 50 different markets, recording the advertising expenditure, social media mentions, and final sales, all measured on an interval scale.

Question:

Which statistical technique would be appropriate for predicting the final sales of the product using advertising expenditure and social media mentions as independent variables?

Problem 7:

You are investigating the effectiveness of a new weight loss drug by comparing the average weight loss of two independent groups: one group taking the drug and the other taking a placebo. The weight loss data is measured on an interval scale.

Question:

Which statistical tool would be most appropriate for comparing the mean weight loss between the group taking the weight loss drug and the group taking the placebo?

Problem 8:

You are interested in examining the relationship between the number of hours of sunlight per day and the growth rate of plants. You collect data from different locations, recording sunlight hours and plant growth rate, both measured on an interval scale.

Question:

What statistical tool would you use to analyze the relationship between the number of hours of sunlight and the growth rate of plants?

Problem 9:

A researcher wants to explore if there is a significant difference in the average income among individuals with different levels of education (high school diploma, bachelor's degree, and master's degree). Income data is obtained from three independent groups, and it is measured on an interval scale.

Question:

Which statistical test would be appropriate for comparing the average income among individuals with different levels of education?

Problem 10:

You are investigating the association between smoking status (smoker/non-smoker) and the occurrence of respiratory issues in a population. You collect data on smoking status and respiratory issues (present/absent) from a random sample.

Question:

Which statistical test should be used to determine if there is a significant association between smoking status and the occurrence of respiratory issues?

Problem 11:

Three different trainers are providing a fitness program, and you want to assess the agreement among them regarding the fitness improvement scores of participants. The fitness improvement scores are ordinal.

Question:

Which statistical tool is suitable for analyzing the agreement among the three trainers regarding participants' fitness improvement scores?

Problem 12:

You are interested in predicting the average monthly sales of a retail store based on the size of its advertising budget and the number of promotions held in a month. Sales, advertising budget, and number of promotions are measured on an interval scale.

Question:

Which statistical technique would be appropriate for predicting the average monthly sales using advertising budget and the number of promotions as predictors?

Problem 13:

Scenario:

You want to investigate whether there is a significant difference in the average scores of students who attended three different tutoring programs for a standardized test. The scores are measured on an interval scale.

Question:

Which statistical test would be most appropriate for comparing the mean scores among three tutoring programs?

Problem 14:

Scenario:

A company is testing two different packaging designs for a new product to determine which one leads to higher customer satisfaction. Customer satisfaction scores are collected from two independent groups of customers, each exposed to one of the packaging designs. Scores are measured on an interval scale.

Question:

What statistical tool should be used to compare customer satisfaction scores between the two independent groups exposed to different packaging designs?

Problem 15:

Scenario:

You are investigating whether there is a significant difference in the average commute times of employees who use three different modes of transportation: car, public transit, and bicycle. The commute times are measured on an interval scale.

Question:

Which statistical test would be appropriate for comparing the mean commute times among employees using three different modes of transportation?

Problem 16:

Scenario:

A researcher is studying the relationship between the amount of exercise (measured in hours per week) and the body mass index (BMI) of individuals. Both variables are measured on an interval scale.

Question:

What statistical tool would you use to assess the relationship between the amount of exercise and the body mass index?

Problem 17:

Scenario:

You want to assess if there is a significant difference in the average test scores of students before and after they received a special tutoring program. Scores are obtained from the same group of students before and after the tutoring, and they are measured on an interval scale.

Question:

Which statistical test should be used to compare the mean test scores of students before and after the special tutoring program?

Problem 18:

Scenario:

You are studying the association between the type of smartphone (iPhone, Android, or other) and the preference for a particular mobile app. Smartphone type and app preference are categorical.

Question:

Which statistical test should be used to determine if there is a significant association between the type of smartphone and app preference?