significance level

Examples of significance level in the following topics:

• Choosing a significance level

  • Choosing a significance level for a test is important in many contexts, and the traditional level is 0.05.
  • However, it is often helpful to adjust the significance level based on the application.
  • Is there good reason to modify the significance level in such an evaluation?
  • A slightly larger significance level, such as α = 0.10, might be appropriate.
  • Choose a small significance level, such as α = 0.01.

• Significance Levels

  • If a test of significance gives a $p$-value lower than or equal to the significance level, the null hypothesis is rejected at that level.
  • A fixed number, most often 0.05, is referred to as a significance level or level of significance.
  • If a test of significance gives a $p$-value lower than or equal to the significance level, the null hypothesis is rejected at that level.
  • The lower the significance level chosen, the stronger the evidence required.
  • The choice of significance level is somewhat arbitrary, but for many applications, a level of 5% is chosen by convention.

• Using the Model for Estimation and Prediction

  • This is denoted by the significance level of the model.
  • Within the social sciences, a significance level of 0.05 is often considered the standard for what is acceptable.
  • If the significance level is between 0.05 and 0.10, then the model is considered marginal.
  • To see if weight is a "significant" predictor of height, we would look at the significance level associated with weight.
  • Again, significance levels of 0.05 or lower would be considered significant, and significance levels between 0.05 and 0.10 would be considered marginal.

• Was the Result Important?

  • If a test of significance gives a $p$-value lower than or equal to the significance level, the null hypothesis is rejected at that level .
  • Such results are informally referred to as 'statistically significant (at the $p=0.05$ level, etc.)'.
  • For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence", a $0.001$ level of statistical significance is being stated.
  • For example, we could measure two different one-cup measuring cups enough times to find that their volumes are statistically different at a significance level of $0.001$.
  • The difference in this case is statistically significant at a certain level, but not important.

• Was the Result Significant?

  • Popular levels of significance are 10% (0.1), 5% (0.05), 1% (0.01), 0.5% (0.005), and 0.1% (0.001).
  • If a test of significance gives a p-value lower than or equal to the significance level , the null hypothesis is rejected at that level.
  • Such results are informally referred to as 'statistically significant (at the p = 0.05 level, etc.)'.
  • The lower the significance level chosen, the stronger the evidence required.
  • The choice of significance level is somewhat arbitrary, but for many applications, a level of 5% is chosen by convention.

• Testing the Significance of the Correlation Coefficient

  • In this chapter of this textbook, we will always use a significance level of 5%, α = 0.05
  • But the table of critical values provided in this textbook assumes that we are using a significance level of 5%, α = 0.05.
  • If the p-value is less than the significance level (α = 0.05):
  • If the p-value is NOT less than the significance level (α = 0.05)
  • The p-value, 0.026, is less than the significance level of α = 0.05

• Level of Confidence

  • The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
  • The desired level of confidence is set by the researcher (not determined by data).
  • If a corresponding hypothesis test is performed, the confidence level is the complement of respective level of significance (i.e., a 95% confidence interval reflects a significance level of 0.05).
  • In applied practice, confidence intervals are typically stated at the 95% confidence level.
  • However, when presented graphically, confidence intervals can be shown at several confidence levels (for example, 50%, 95% and 99%).

• Type I and II Errors

  • Explain why the null hypothesis should not be accepted when the effect is not significant
  • The threshold for rejecting the null hypothesis is called the α (alpha) level or simply α.
  • It is also called the significance level.
  • The Type I error rate is affected by the α level: the lower the α level, the lower the Type I error rate.
  • Lack of significance does not support the conclusion that the null hypothesis is true.

• Significance Testing

  • The probability value below which the null hypothesis is rejected is called the α level or simply α.
  • It is also called the significance level.
  • Do not confuse statistical significance with practical significance.
  • The alternative approach (favored by the statisticians Neyman and Pearson) is to specify an α level before analyzing the data.
  • Therefore, if the 0.05 level is being used, then probability values of 0.049 and 0.001 are treated identically.

• Tests of Significance

  • The statistical significance of the results depends on criteria set up by the researcher beforehand.
  • However, conventional thresholds for significance may vary depending on disciplines and researchers.
  • For example, health sciences commonly settle for 10% ($\text{sig} \leq 0.10$), while particular researchers may settle for more stringent conventional levels, such as 1% ($\text{sig} \leq 0.01$).
  • Assuming a conventional 5% level of significance ($\text{sig} \leq 0.05$), all tests are, thus, statistically significant.
  • Examine the idea of statistical significance and the fundamentals behind the corresponding tests.