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Part IV Significantly Different: Using Inferential Statistics

Part IV Significantly Different: Using Inferential Statistics. Chapter 9   Significantly Significant: What it Means for You and Me. The Concept of Significance. Any difference between groups that is due to a systematic influence rather than chance

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Part IV Significantly Different: Using Inferential Statistics

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  1. Part IVSignificantly Different:Using Inferential Statistics Chapter 9   Significantly Significant: What it Means for You and Me

  2. The Concept of Significance • Any difference between groups that is due to a systematic influence rather than chance • Must assume that all other factors that might contribute to differences are controlled

  3. If Only We Were Perfect… • Significance level • The risk associated with not being absolutely sure that what occurred in the experiment is a result of what you did or what is being tested • The goal is to eliminate competing reasons for differences as much as possible. • Statistical Significance • The degree of risk you are willing to take that you will reject a null hypothesis when it is actually true.

  4. The World’s Most Important Table

  5. Type I Errors (Level of Significance) • The probability of rejecting a null hypothesis when it is true • Represented by alpha () • Conventional  levels are set between .01 and .05 • Choice of alpha often depends on the consequences of being wrong

  6. Type II Errors • The probability of accepting a null hypothesis when it is false • Referred to as “Beta” • Represented by β • Power = 1- β

  7. Significance Versus Meaningfulness • A finding can be statistically significant but not very meaningful • A finding can be statistically significant but not “big enough” • Statistical significance should not be the only goal of scientific research • Effect Size • Significance is influenced by sample size and variability…we’ll talk more about this later.

  8. How Inference Works • A representative sample of the population is chosen. • Data is collected, a mean (or means) are computed and compared to population means (real or hypothesized) • A conclusion is reached as to whether the mean is statistically significant (i.e. different from the population mean) • Based on the results of the sample, an inference is made about the population.

  9. Deciding What Test to Use

  10. Tests of Significance – A General Process 1. A statement of the null hypothesis. 2. Set the level of risk associated with the null hypothesis. (alpha) 3. Select the appropriate test statistic. 4. Compute the test statistic (obtained) value 5. Determine the value needed to reject the null hypothesis using the appropriate table of critical values 6. Compare the obtained value to the critical value 7. If obtained value is more extreme, reject the null hypothesis 8. If obtained value is not more extreme, accept the null hypothesis

  11. The Picture Worth a Thousand Words

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