Lecture on Inferential Statistics

Introduction

• Inferential statistics is often challenging for students but crucial for exams.
• Importance: Questions on statistics can yield high marks with minimal writing.
• Focus: The sign test is the only statistical test you'll need to calculate for AQA exams.

What are Inferential Statistics?

• Descriptive Statistics: Summarize and describe raw data (e.g., central tendency, dispersion).
• Inferential Statistics: Generalize results from a sample to a target population.
  • Involves making inferences about the entire target population.
  • Based on probability; significant if p < 0.05.

Deciding Which Statistical Test to Use

• Stem: Scenario given before the question to determine the statistical test needed.
• Correlation vs. Test of Difference: Determine the type of study.
  • Correlation: Looks for a relationship between two covariables.
  • Test of Difference: Tests for differences due to manipulation of independent variables.
• Experimental Design: Independent groups vs. repeated measures vs. match pairs.
  • Independent groups = unrelated data.
  • Repeated measures/Matched pairs = related data.
• Levels of Measurement: Nominal, ordinal, interval (ratio treated as interval).

Statistical Tests Table

• Memorize the appropriate statistical test for each combination of data type and design.
• Mnemonic: "Space weather really contains many UFOs chasing small pigs" for remembering test initials.

Examples and Application

• Practice identifying the correct test from given study scenarios.
• Justify the choice of test based on the test of difference, type of data, and level of measurement.

Answering Stats Questions

• Structure answers to maximize exam marks.
  • Name the test, justify choice with: test type, data type, measurement level.
• Critical Values Table: Use to determine data significance.
  • Compare calculated value to critical value using sample size and significance level.

Calculating the Sign Test

• When to Use: Repeated measures/match pairs design, nominal data.
• Process:
  • Subtract scores between conditions.
  • Record the sign (positive/negative) for each subtraction.
  • Calculate N (number of differences) and S (least frequent sign).
• Significance: Compare calculated S to critical value for significance.

Conclusion

• Practice with mock questions to identify statistical tests and justify choices.
• Utilize resources such as tutorial videos and printable materials for further study.
• Acknowledgment of support from Patreon and the importance of ongoing learning.