Question

What are the five components of a statistical test and give a brief description and examples of each?

Answer 1

Ans. COMPONENTS OF A STATISTICAL TEST:-

1. Null and alternative hypothesis

1. The null hypotheses (H₀) is a statement that the value of a population parameter (mean) is equal to some claimed value. Ex H_0: µ=98.6
2. The alternative hypotheses (H₁ or Ha) is the statement that the parameter has a value that somehow differs for the null hypothesis. For the methods of this course, the symbolic form of the alternative hypothesis must use one of these symbols: < or > for directional test, or ≠ for non-directional test.

Directionality

• Non-directional tests (two-tailed test)

H_a: (one sample), (two samples)

Example keywords: compare, change, difference, etc

• Directional tests (one-tailed test)

   H_a: > (or <) (one sample) > (or <) (two samples)

Example keywords: reduce, improve, delay, raise, higher, lower, greater than, etc

2. Significance level (denoted by α).

Baseline of rejection probability; Probability that the test statistic will fall in the critical region when the null hypothesis is actually true. If the test statistic falls in the critical region, we will reject the null hypothesis, so α is the probability of making the mistake of rejecting the null hypothesis when it is true.

3. Test Statistics

The test statistics is a value computed from the sample data, and it is used in making the decision about the rejection of the null hypothesis. The test statistic is found by converting the sample statistic (such as the sample mean) to a score (such as t) with the assumption that the null hypothesis is true. The test statistics can therefore be used for determining whether there is significant evidence against the null hypothesis.

4. Critical Region, Critical Value and P-Value

• Critical region- The critical region (or rejection region) is the set of all values of the test statistic that cause us to reject the null hypothesis.
• Critical Value- A POSITIVE value that decides that boundary of the critical region. The critical value changes depending on the directionality.
• P-Value- The probability of getting a value of the test statistic that is at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

5. Decision

Reject H₀, when,

• Test Statistics > Critical Value (positive)
• Test Statistics < Critical Value (negative)
• P-value < (alpha)