Guide to Choosing Statistical Tests

Aug 11, 2024

Choosing Which Statistical Test to Use

Introduction

  • Many statistical tests exist, can be difficult to choose the right one.
  • Focus on 7 common tests involving means, proportions, and relationships.
  • Three key questions to determine the appropriate test:
    1. What level of measurement was used for the data?
    2. How many samples do we have?
    3. What is the purpose of our analysis?

Key Questions Explained

1. Level of Measurement

  • Nominal Data (Categorical/Qualitative/Nonparametric)
    • Examples: Color, defective parts, preferred type of chocolate.
    • Summary Values: Frequencies, proportions, percentages.
    • Tests: Proportion, difference of two proportions, chi-squared test for independence.
  • Interval/Ratio Data (Quantitative)
    • Examples: Daily sales figures, weight, temperature.
    • Summary Value: Mean.
    • Tests: Mean, difference of two means (independent/dependent), regression analysis.
  • Ordinal Data
    • Classified with nominal or interval/ratio depending on circumstances.

2. Number of Samples

  • One Sample
    • Testing a statistic against a hypothesized value.
  • Two Samples
    • Comparing two different groups (e.g., men vs. women).
  • One Sample with Two Variables
    • Same sample measured twice (e.g., sales figures and temperature).

3. Purpose of Analysis

  • Testing Against a Hypothesized Value
  • Comparing Two Statistics
  • Looking for a Relationship
    • Chi-square test for independence (data summarized in a table).
    • Regression analysis (data on a scatter plot).

Examples of Tests

  1. Test for a Mean
    • Example: Helen measures the weight of nuts in choconutties.
    • Data: Interval/Ratio.
    • Samples: One sample of 20 packets.
    • Purpose: Comparing against a given value.
  2. Test for a Proportion
    • Example: Helen checks if 20% of choconutties packets have prize tickets.
    • Data: Nominal.
    • Samples: One sample of 50 packets.
    • Purpose: Comparing sample value against a given value.
  3. Difference of Two Means (Paired Sample)
    • Example: Comparing eating times of choconutties and nutta bars.
    • Data: Interval/Ratio.
    • Samples: One sample of 36 people with two scores each.
    • Purpose: Looking for a difference in times.
  4. Difference of Two Proportions
    • Example: Comparing defective wrapping from two machines.
    • Data: Nominal.
    • Samples: Two independent samples (200 bars from one machine, 150 from another).
    • Purpose: Comparing proportions.
  5. Difference of Two Means (Independent Samples)
    • Example: Comparing sales figures with/without free stickers.
    • Data: Interval/Ratio.
    • Samples: Two samples (13 days with stickers, 10 days without).
    • Purpose: Comparing average sales figures.
  6. Regression
    • Example: Relationship between temperature and sales.
    • Data: Interval.
    • Samples: One sample of 30 days with two measures each.
    • Purpose: Looking for a relationship.
  7. Chi-squared Test for Independence
    • Example: Chocolate preference by gender.
    • Data: Nominal.
    • Samples: One sample of 50 customers with two measures each.
    • Purpose: Looking for a relationship.

Conclusion

  • Numerous other statistical tests exist.
  • This summary covers 7 basic tests and helps in deciding which test to choose based on the level of measurement, number of samples, and purpose of analysis.