What is Hypothesis Testing?

Hypothesis Testing

         We have considered many problems of the point estimate and interval estimate involving unknown parameters such as means and proportions. In this chapter, we must deal with a decision-making process in which we must come to some conclusion about unknown population parameters the so-called testing of hypothesis. A hypothesis is widely used in science and research. In this subject, a hypothesis is used to mean a statistical hypothesis. A statement, an assertion, conjecture, or an assumption concerning one or more population. 

          In hypothesis testing, the researcher must define the population under study, state the particular hypotheses to be investigated, giving the significance level, select a sample statistic, perform the required test and make conclusions. There are two specific statistical tests for hypothesis testing on means: the z test and the t-test. 

          Hypothesis testing is a technique for determining whether a research hypothesis is justified in the light of observed data and is considered the primary tool for making decisions based on statistical analysis.

Basic Concepts of Types of Hypothesis

Null Hypothesis

    

          This is a statement that specifies some aspects of a population that is known or assume to be true. It is always stated as an equality so as to specify an exact value of the parameter. This means that the null hypothesis statement is describe of “no significant difference, no significant effect, no significant relationship, no significant association” on whatever phenomena the researcher wants to test. Usually, the null hypothesis is denoted by Ho. 

Alternative Hypothesis

          This is called the research hypothesis, it is a statement that contradicts the null hypothesis, that is, a statement of “significance”. Usually, the alternative hypothesis is denoted by Ha or .

Type of Tailed Test

One-Tailed test or Directional test

          A one-tailed test indicates that the null hypothesis should be rejected when the computed test value is in the critical region on one side of the parameter. A one-tailed test is either right-tailed when the inequality in the alternative hypothesis is greater than (>) or left-tailed when the direction is less than (<).

Two-Tailed test of Non-directional test

          In this test, the null hypothesis should be rejected when the test value is in either of the two critical regions or the rejection region. 

Critical Region or Rejection Region

          This is a portion of the sampling distribution of the test statistic which comprises the set of all values of the test statistic that would justify rejecting the null hypothesis in favor of its alternative. 

Critical Value

          This is a value selected from a table for the appropriate test statistic. This determines or divides the acceptance and the rejection region. 

Test Statistic

This is a value obtained after computed from sample data.

Level of Significance

          This is a probability value which specifies the risk of incorrectly rejecting the null hypothesis when it is true. The level of significance is predetermined or set by the researcher beforehand. This is symbolized by α (a Greek letter alpha).

Types of Error in Hypothesis testing

          Since the decision on the null hypothesis is based on sample data, there is a probability of drawing incorrect conclusions from the evidence available. Researchers may commit these types of errors in the decision of rejecting or accepting the null hypothesis. These are the Type I error and Type II error. 

Type I Error

This is the error committed in rejecting the null hypothesis Ho when, in fact, it is true.

Type II Error

This is the error committed in accepting the null hypothesis Ho when, in fact, it is falls.

          The classical approach to hypothesis testing uses the critical value criterion for significance. These critical values are also called tabular values since they are obtained from statistical tables of various probability distribution such as the Table of t-distribution and the z – distribution to name a few.

Steps in Classical Hypothesis Testing

Step 1. State the null hypothesis, Ho and alternative hypothesis Ha.

Step 2. Set the level of significance of the test, α.

Step 3. Select an appropriate test statistic and establish the critical region.

Step 4. Compute the value of the test statistic.

Step 5. Make a decision concerning the null hypothesis.

Step 6. Draw a conclusion concerning the population.

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For more details and illustration about hypothesis testing go to my next discussion on the illustrations on hypothesis testing.