LEVEL OF SIGNIFICANCE.pptx
- 2. Level of Significance The level of significance, also denoted as alpha or 𝛼, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant. The researcher determines the significance level before conducting the experiment. To obtain the level of significance use the formula 𝛼=1− confidence level.
- 3. Types of Errors •Type I Error: If the null hypothesis is true and rejected, the decision is incorrect. •Type II Error: If the null hypothesis is false and accepted, the decision is incorrect.
- 4. EXAMPLE •A person is on trial for a criminal offense and the judge needs to provide a verdict on his case. Now, there are four possible combinations in such a case:
- 5. Error in Decision Type Probability Reject a true Ho I 𝛼 Accept a false Ho II 𝛽 Correct Decision Type Probability Accept a true Ho A 1−𝛼 Reject a false Ho B 1−𝛽 As shown above, two possible errors could be committed. The probability of committing Type I error is represented by 𝛼 (Greek letter alpha), while the probability of committing a Type II error is denoted as β (Greek letter beta
- 6. Rejection Region Graphically we can show the decision errors under the normal curve. Note that the rejection region for a directional test is in one tail (Figure 1) but distributed to the two tails in a non -directional test (Figure 2). Under the normal curve, the rejection region refers to the region where the value of the test statistic lies for which we will reject the null hypothesis. This region is also called critical region. So, if your computed statistic is found in the rejection region, then you reject Ho . It is found outside the rejection region, you accept Ho. (Figure 1) (Figure 2)
- 7. Population Population – refers to the totality of objects, individuals, characteristics, or reactions of interest (e.g. based on the total count of votes in the national level Grace Poe was proclaimed as the number 1 senator.) Sample – is a group of subjects carefully selected from a population of interest (e.g. As of May 15, 8:15pm, 10% of the votes have been counted and Nancy Binay is in the 5th spot.) Parameter – is the numerical value that describes characteristics of a population (e.g. total votes) Statistic – is the numerical value that describes a particular sample (e.g. 10% of votes)
- 8. Sample • Sample – is a group of subjects carefully selected from a population of interest. (e.g. As of May 15, 8:15pm, 10% of the votes have been counted and Nancy Binay is in the 5th spot.)
- 9. Parameter – is the numerical value that describes characteristics of a population (e.g. total votes)
- 10. Statistic Statistic – is the numerical value that describes a particular sample (e.g. 10% of votes)
- 11. Activity: Identify the term that is being described in the given statement. ___________________ 1. Accepting a false null hypothesis. ___________________ 2. Rejecting a true null hypothesis. ___________________ 3. The region where the value of the test statistic lies for which we will reject the null hypothesis. ___________________ 4. It is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant. ___________________ 5. It refers to the probability of committing a type I error.