Statistical Tests: Choosing which statistical test to use

Summary

This video explains how to choose the right statistical test by considering three key questions: the level of measurement of the data, the number of samples involved, and the purpose of the analysis. It covers seven common statistical tests, including tests for means, proportions, and relationships between variables. The video provides practical examples, such as testing the weight of choconutties, comparing prize ticket proportions, and analyzing the impact of stickers on sales. With clear guidance on when to use tests like regression or chi-squared, it equips viewers with essential tools for making data-driven decisions.

Takeaways

• 😀 Understanding which statistical test to use starts with asking three key questions: level of measurement, number of samples, and the purpose of the analysis.
• 📊 Data can be categorized as nominal (qualitative) or interval/ratio (quantitative). Nominal data is used in tests like proportions and chi-squared tests, while interval/ratio data is used in mean and regression tests.
• 🔢 When analyzing data, you must first determine if it is nominal or interval/ratio, as this will dictate the type of test to use.
• 📉 Tests like the chi-squared test for independence are used for nominal data, while tests like regression analysis are applied to interval/ratio data for assessing relationships.
• 🧑‍🤝‍🧑 The number of samples plays a crucial role in choosing the test. A single sample leads to one-sample tests, while comparing two groups requires two-sample tests.
• 🔄 For comparing paired data (e.g., before and after measurements on the same group), use paired sample tests for comparing means or other variables.
• 🔍 The purpose of analysis helps determine if you're testing a value against a hypothesized value, comparing two statistics, or analyzing relationships between variables.
• 🧾 Example 1: If you're testing the weight of choconutties against a known value, you’d use a one-sample test for a mean.
• 🎟 Example 2: When checking the proportion of choconutties with winning tickets, use a one-sample test for proportions.
• 🏆 Example 3: To compare the longevity of choconutties and nuttabars, use a paired sample test for the difference in means.
• 🔧 Example 4: If comparing the defective wrapping between two machines, a test for the difference of two proportions is appropriate.
• 🎁 Example 5: To test if stickers affect sales, compare the sales means between two independent groups with a two-sample mean test.
• 🌡️ Example 6: When looking for a relationship between temperature and sales, use regression analysis to explore the correlation.
• 🍫 Example 7: For testing the relationship between gender and chocolate preferences, use the chi-squared test for independence.

Q & A

What are the three key questions to ask when deciding which statistical test to use?

The three key questions are: 1) What level of measurement was used for the data? 2) How many samples do we have? 3) What is the purpose of the analysis?

How does the level of measurement affect the choice of statistical test?

The level of measurement determines the type of test to use. Nominal data, such as categories or counts, typically requires tests for proportions, while interval/ratio data, which involves numerical values, often requires tests for means or regression analysis.

What is nominal data and what tests are used with it?

Nominal data is categorical and non-numeric, such as types of chocolate or defective/non-defective items. Tests used for nominal data include the test for a proportion, difference of two proportions, and chi-squared test for independence.

What is interval/ratio data and what tests are associated with it?

Interval/ratio data is quantitative and involves continuous variables, such as weight, temperature, or sales figures. Tests for this type of data include the test for a mean, difference of two means (independent or paired), and regression analysis.

What is the difference between one sample and two samples in statistical testing?

In one sample, the analysis involves testing a single group's data against a hypothesized value. In two samples, the analysis compares data from two independent or related groups to see if there are differences or relationships.

What is the purpose of comparing proportions in statistical tests?

The purpose of comparing proportions is to determine if the proportions (or percentages) of a characteristic in two samples are significantly different, such as comparing defect rates between two machines or success rates of two treatments.

What does the chi-squared test for independence measure?

The chi-squared test for independence measures the relationship between two categorical variables. It determines whether the distribution of one variable is independent of the distribution of another.

How is regression analysis used in statistical testing?

Regression analysis is used to examine the relationship between two interval/ratio variables. It helps in understanding how one variable (e.g., temperature) influences another (e.g., sales).

What is the difference between a paired sample and an independent sample test?

A paired sample test compares two related variables from the same sample, such as before-and-after measurements. An independent sample test compares two separate groups, such as men versus women or two different treatments.

What statistical test would Helen use to determine if the sales of choconutties are affected by temperature?

Helen would use regression analysis because she is looking to analyze the relationship between two interval/ratio variables: temperature and sales.