The principle of checking the hypothesis is relatively straightforward. We observe certain events in different studies. We have to wonder, is the incident simply attributable to chance, or is there any explanation we should be searching for? We need a way to distinguish between events that easily happen by chance and events that are highly unlikely to happen spontaneously. Such a method should be streamlined and well defined so that our statistical experiments can be replicated by others.
Hypothesis experiments are performed using a few different methods. One of these approaches is referred to as the traditional method and another uses what is known as a p-value. The steps of these two most common methods are identical up to a point, then diverge slightly. However, all tests of hypothesis are carried out almost in the same manner. The researcher states a hypothesis to be tested, formulates a plan of analysis, analyzes sample data according to plan, and accepts or rejects the null hypothesis based on analysis results.
The Steps to Testing a Hypothesis
The aim of hypothesis testing is to evaluate the probability that a variable of the population, such as the mean, is likely to be true.
Step 1: State the hypotheses.
Step 2: Set the criteria for a decision.
Step 3: Compute the test statistic.
Step 4: Make a decision.
Step 1: State the hypothesis. -
Hypothesis test requires a null hypothesis and an alternative hypothesis to be specified by the analyst. The hypotheses are stated in such a way as to exclude each other. That is, the other must be false if one is true; and vice versa.
Formulate a plan for the study. The study strategy explains how the null hypothesis can be accepted or rejected using sample data. The following elements should be listed.
Significance level. Researchers often choose meaning levels equal to 0.01, 0.05, or 0.10, but it is possible to use any value between 0 and 1.
Step 2: Test Method:
This typically involves test statistics and the distribution of samples. The test statistics, calculated from sample data, could be a mean score, ratio, difference between values, the difference of proportions, z-score, t statistics, chi-square, etc. A researcher may determine the probabilities associated with the test statistics based on test statistics and its sampling distribution. If the likelihood of the test result is less than the degree of significance, the null hypothesis will be dismissed.
Step 3: Calculate the Stats for the Test
Suppose we measure an average sample of 4 hours per week that children watch television. To make a decision, we need to assess the likelihood of this sample outcome if the mean population of the null hypothesis (3 hours per week) is true. To determine this likelihood, we use test statistics. Essentially, research statistics show us how far a sample mean from the population means, or how many standard deviations. The higher the test statistics value, the lower the range or number of standard deviations, the higher the sample mean is from the null hypothesis population mean.
Step 4: Make a decision.
We make a decision on the null hypothesis using the importance of the test statistics. The decision is based on the probability that a sample mean will be obtained, since the value stated in the null hypothesis is true. If, when the null hypothesis is valid, the likelihood of achieving a sample mean is less than 5%, then the decision is to reject the null hypothesis. When, when the null hypothesis is valid, the likelihood of achieving a sample mean reaches 5 percent, then the decision is to hold the null hypothesis. In summary, two decisions can be made by a researcher:
1. Reject the hypothesis that is null When the null hypothesis is valid, the test mean is correlated with a low probability of occurrence.
2. Retain the null hypothesis: When the null hypothesis is valid, the test mean is correlated with a high probability of occurrence.
Because the value stated in the null hypothesis is true, the probability of obtaining a sample mean is stated by the p value. The p value is a likelihood: it ranges from 0 to 1 and can never be negative. In Step 2, we stated the criterion or likelihood of obtaining a sample mean at which point we will decide to reject the value stated in the null hypothesis, which is typically set at 5% in behavioral research.
To make a decision, we compare the p value to the criterion we set in Step 2.
When the p value is less than 5% (p < .05), we reject the null hypothesis. We will refer to p < .05 as the criterion for deciding to reject the null hypothesis, although note that when p = .05, the decision is also to reject the null hypothesis. When the p value is greater than 5% (p > .05), we retain the null hypothesis. The decision to reject or retain the null hypothesis is called significance. When the p value is less than .05, we reach significance; the decision is to reject the null hypothesis. When the p value is greater than .05, we fail to reach significance; the decision is to retain the null hypothesis. Figure 8.3 shows the four steps of hypothesis testing.