Hypothesis testing is a statistical approach employed to draw conclusions about a population based on data obtained from a sample. This process entails the formulation of a null hypothesis and an alternative hypothesis and assessing the probability of observing the data under the assumption that the null hypothesis is valid. The outcomes of these tests provide insights into whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
Consider a scenario where a nutritional program has implemented a new diet to improve children’s health. The program asserts that this new diet has led to an increase in the average weight of the children. In this case, the null hypothesis (H0) posits that the average weight of the children remains unchanged following the introduction of the new diet, while the alternative hypothesis (H1) suggests that the average weight of the children has indeed increased as a result of the new diet.
What is one-tailed/two-tailed test?
One-tailed and two-tailed tests represent distinct categories of hypothesis tests utilized in inferential statistics to evaluate the significance of relationships or differences within data. A one-tailed test is characterized by its directional nature, as it predicts an outcome in a specific direction (for instance, greater than or less than a particular value). This type of test is appropriate when researchers possess a clear expectation regarding the direction of the relationship or difference between the variables in question. Conversely, a two-tailed test is non-directional, meaning it does not indicate a specific expected direction for the relationship or difference. Instead, it assesses the potential for a relationship or difference to exist in either direction. The decision to employ a one-tailed or two-tailed test is contingent upon the research question, the specific hypothesis under examination, and the anticipated directionality of the relationship.
Let us denote the average weight of children before the new diet as μ1 and the mean weight following the new diet as μ2.
One-tailed test: (A researcher aims to determine if the new diet leads to an improvement in the average weight of children when compared to the previous diet. |)
H0: The new diet does not improve the average weight of children (μ2 ≤ μ1).
H1: The new diet significantly improves the average weight of children (μ2 > μ1).
Two-tailed test: A researcher seeks to investigate whether there is a difference in the average weight of children before and after the implementation of the new diet.
H0: There is no difference in the average weight of children before and after the new diet (μ2 = μ1).
H1: There is a significant difference in the average weight of children before and after the new diet (μ2 ≠ μ1).
