Lecture Notes: Inferential Statistics

Introduction to Inferential Statistics

• Inferential statistics often dreaded by students.
• Exam questions on statistics can yield high points for minimal writing.
• Focus on using the Sign Test for AQA exams; know names and usage for other seven tests.

Understanding Inferential Statistics

• Descriptive Statistics vs. Inferential Statistics
  • Descriptive: Measures central tendency or dispersion to summarize raw data.
  • Inferential: Generalizes results beyond the sample, making inferences about a target population.
  • Decision based on probability: Likelihood of results being due to chance should be less than 1 in 20 (p < 0.05).

Statistical Tests and Exam Tips

• Deciding on a Statistical Test

  • Determine if the study is a correlation or a test of difference.
  • Correlation: Look for terms like correlation, relationship, association.
  • Test of Difference: Involves manipulating the independent variable to observe effects on the dependent variable.
  • Experimental Design: Independent groups (unrelated data), repeated measures, or matched pairs (related data).

• Levels of Measurement

  • Nominal: Data in categories.
  • Ordinal: Data in order.
  • Interval: Equal differences between data points (Ratio treated as interval).

• Memorization Strategy

  • Use phrases to memorize the order of statistical tests.
  • Example: "Space weather really contains many UFOs chasing small pigs."

Conducting Statistical Tests

• Test Selection Process

  • Correlation studies use tests in the bottom row of the table.
  • Experimental (test of difference) studies use tests in top two rows.
  • Use table to choose based on type of study, design, and level of measurement.

• Examples of Statistical Test Application

  • Match study scenarios to appropriate statistical tests using memorized table.
  • Justify selection by describing design, data type, and measurement level.

Answering Stats Questions in Exams

• Common Question Types

  • Name the appropriate test and justify choice.
  • Explain why a specific test is suitable.

• Calculating Significance

  • Use critical values table to determine significance.
  • Understand 1-tailed vs. 2-tailed tests and their relation to directional hypotheses.

Working with Degrees of Freedom

• Chi-Square Test and Degrees of Freedom
  • Calculate using formula: (Rows - 1) x (Columns - 1).
  • Use degrees of freedom to find critical value.

Calculating the Sign Test

• Process for Sign Test Calculation
  • Test of difference (experiment), repeated measures or matched pairs, nominal level.
  • Steps: Subtract scores, record signs, calculate N (with differences) and S (least frequent sign).
  • Use critical value table to determine significance.

Conclusion

• Practice using the statistical test table and calculation methods.
• Utilize tutorial videos and resources available for further study and exam preparation.
• Acknowledgment of support from patrons and students.