# What is Hypothesis Testing in Statistics?

From the word in Greek, hypothesis can be interpreted as a statement that is still weak in truth and needs to be proven.

According to William G. Zikmund in his book entitled Business Research Methods, it is explained that a hypothesis is a proposition that has yet to be scientifically proven. So, this proposition must be proven empirically with a research process following the appropriate methodology.

A hypothesis is a quick answer to a problem in the form of a scientific conjecture (not arbitrary). The truth must be proven first and then through research or research.

So there are at least three keywords in understanding the hypothesis:

• Scientific suspicion
• Temporary
• Needs to be tested or proven.

## Hypothesis Testing

Hypothesis Testing is a branch of Inferential Statistics used to statistically test the truth of a statement and draw conclusions about whether to accept or reject the idea.

Brief statements or assumptions made to be tested for validity are called hypotheses or hypotheses.

The purpose of Hypothesis Testing is to establish a basis so that it can collect evidence in the form of data in determining whether to reject or accept the truth of the statements or assumptions made.

Hypothesis testing can also provide confidence in objective decision-making.

Examples of Hypothesis Statements that must be tested for validity include:

• Soldering Machine 1 is better than Soldering Machine 2
• New method can produce higher Output
• The new chemicals are safe and usable

## Hypothesis Testing Statement

#### 1. The Null Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study’s outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

Key features:

• Statements are assumed to be valid unless there is strong evidence to disprove them.
• Always contain the statements “equals,” “No effect,” “No difference.”
• Denoted by H0
• Example: H0 : μ1 = μ2 or H0 : μ1 ≥ μ2

#### 2. The Alternate Hypothesis

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

The statement is valid if the Null Hypothesis (H0) is successfully rejected.

• Denoted by H1 or HA
• Example H1 : μ1 ≠ μ2 or H1 : μ1 > μ2

## Hypothesis Testing Stages

The purpose of hypothesis testing is to decide whether the hypothesis being tested is rejected or accepted. Technically, hypothesis testing is carried out to determine whether the parameter differs from the value in the null hypothesis.

If the data is significantly different, assuming the null hypothesis is true, then the null hypothesis is rejected.

Hypothesis testing stages can start from:

### 1. States The Hypotheses

In testing the hypothesis, we will face two types of premises. The two types of hypotheses are:

null hypothesis (Ho)

alternative hypothesis (Ha)

The first step in hypothesis testing is to change the research question into the initial idea or null hypothesis (Ho) and the alternative Hypothesis(Ha).

The null and alternative hypotheses are concise statements, usually mathematical sentences, about relationships between predictors in the population.

The null and alternative hypotheses must be complete (i.e., include all possible truths) and mutually exclusive (i.e., not overlap).

Example:

Let’s say we are interested to see if there is a difference in the height of grade III students between female and male students at Wanokuni Middle School?

The formulation of the problem can be made through research questions as follows.

Is there a difference in the height of the third-grade students between female and male students at Wanokuni Middle School?

From these questions, we can make the following hypothesis.

Ho: There is no difference in height between male and female students

Ha: There is a difference in height between boys and girls.

Or it can also be written as:

Ho: Height of male students = height of female students

Ha: Height of boy student =/ height of the girl student.

### 2. Collecting Data

For a statistical test to be valid, it is vital to collect data by survey or sampling in a way designed to test our hypothesis.

If the data we use is not representative, we cannot make statistical conclusions about the population we are testing.

To see the differences between the height of boys and girls, our sample must have the same proportion of boys and girls and include any other variables that might affect the average size.

We must also consider the scope of our study, as this can also affect the results of the analysis. In the case example we use, it is clear that the area of study is Wanokuni Middle School. We are not interested in students in other schools.

### 3. Determine Significance Level

What is the level of significance or significance level?

The significance level is the chance that the event will occur by chance. If the level is low enough, the probability of chance occurrence is small enough. We say the event is significant.

The significance level indicates the probability of making the wrong decision when the null hypothesis is true.

The significance level (denoted by the Greek letter alpha—a) is generally set at 0.05.

We can conclude that there is a 5% chance that we will accept the alternative hypothesis when our null hypothesis is true.

The smaller the level of significance, the greater the burden of proof needed to reject the null hypothesis, or in other words, to support the alternative hypothesis.

### 4. Determine the test criteria and rejection area

The test statistic determines the hypothesis test, which is a function of the sample data, and the critical area. The null hypothesis is rejected if the value of the test statistic is in the critical region and is not dismissed otherwise.

The rejection or critical area is the set of all statistical test values that cause the null hypothesis to be rejected.

The critical area is chosen so that the probability of rejecting the null hypothesis when it is true is not greater than a predetermined value (significance level). The rejection area is determined from our alternative hypothesis.

Alternative hypotheses can be divided into:

• two-sided (two-tailed)
• one side (right side and left side)

Thus, the area of rejection is made by adjusting the alternative hypotheses, which can be two-sided or one-sided.

Suppose the alternative hypothesis has an unequal formulation. In that case, two critical areas are obtained at the ends of the distribution, namely the right and left.

The area of the crucial area or rejection area at each end is 1/2 α because there are two rejection areas.

The test criterion for this process is Ho rejected if the statistic calculated based on the sample is not less than the positive rejection area (right) and not more than the left negative rejection area. The test for this is called a two-tailed test.

Whereas for the alternative hypothesis, which has a larger or smaller formulation, the distribution is obtained from a critical area located at the right or left end. The acute/rejection area is α.

Test criteria: reject Ho if the statistics calculated based on the sample are equal to the rejection area. Testing for this is called a one-tailed test.

### 5. Select and Perform Statistical Testing

Statistical testing aims to decide whether there is sufficient evidence from the sample under study to conclude alternative hypothesis should be trusted.

Hypothesis testing generally uses statistical tests comparing groups or the relationship between variables. Confidence intervals are usually used when describing a single sample without establishing relationships between variables.

Various statistical tests are available, but all are based on a comparison of within-group variance (how to spread out the data in a category) to between-group variance (how different the types are from one another).

Suppose the variance between groups is large enough that there is little or no overlap between groups. In that case, the statistical test will show a low p-value. It is unlikely that the differences between these groups arose by chance.

Or, if there is high within-group variance and low between-group variance, then the statistical test will reflect this with a high p-value. Any differences we measure between groups are likely due to chance.

How to choose a statistical test?

The selection of statistical tests is based on

Types of data we collect

Distribution assumptions

### 6. Making Conclusion

Based on the results of statistical tests, we have to decide whether the null hypothesis is supported or rejected.

If the null hypothesis is rejected, this result is interpreted as consistent with our alternative hypothesis.