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Key Insights on Inferential Statistics

Sep 12, 2024

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.