The formal technique of using statistics to test our worldviews is called hypothesis testing. Scientists use it most frequently to investigate specific predictions drawn from theories, or hypotheses.
The five main steps in hypothesis testing are as follows:
- Declare a null hypothesis (Ho) and an alternative hypothesis (Ha or H1) for your investigation.
- Gather information in a way that will enable you to test the theory.
- Perform an appropriate statistical test.
- Deciding whether to reject your null hypothesis is up to you.
- Present your conclusions in the results and discussion section.
The method you use to test a hypothesis will always involve some variation of these stages, even though the specifics may vary.
Step 1: Identify your null and backup hypotheses
In order to evaluate your initial research hypothesis (the prediction you wish to investigate) quantitatively, you must rewrite it as a null (Ho) and alternate (Ha) Hypothesis Testing.
Your alternate hypothesis is typically your first hypothesis, which assumes a relationship exists between the variables. According to the null hypothesis, there should be no correlation between the relevant variables.
An illustration of a hypothesis test
Check to determine whether there is a correlation between height and gender. Based on your understanding of human physiology, you postulate that men are typically taller than women. Let’s repeat this claim in order to test it:
- H0: Men and women are around the same height on average.
- Typically, guys are taller than women.
Step 2: Compile data
Data collection and sampling must be done in a way that is intended to evaluate your hypothesis for a statistical test to be considered valid. If your data are not representative of the population you are interested in, you cannot draw any statistical conclusions about it.
An illustration of a hypothesis test
Your sample should consist of an equal number of men and women, as well as individuals from various socioeconomic levels and any other relevant control variables, in order to assess the variations in average height between men and women.
Additionally, consider your scope (is it global? for only one nation?) Census data, which is available for many nations worldwide and includes information from a variety of locations and socioeconomic groupings, could be a good data source in this case.
Step 3: Run a statistical analysis
Other statistical tests are available, but they all contrast between-group variance (how dissimilar the categories are from one another) and within-group variance (how dispersed the data is within a category).
Your statistical test will show a low p-value if the between-group variance is so great that there is little to no overlap across groups. This shows that it is unlikely that the differences between these groups are the result of accident.
In contrast, your statistical test will display a high p-value if there is a significant within-group variance and a low between-group variance. This implies that any differences you discover between groups are most likely the result of chance.
Your choice of statistical test will depend on the range of variables and the degree of measurement of your data.
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An illustration of a hypothesis test
Based on the type of data you gathered, you utilize a one-tailed t-test to ascertain whether men are in fact taller than women. You can estimate the average height difference between the two groups using this test.
A p-value that shows how likely it is that this difference will exist if the null hypothesis that there is no difference is correct.
The average heights of men and women, according to your t-test results, are 175.4 cm and 161.7 cm, respectively, with an estimated actual difference that ranges from 10.2 cm to infinity. The p-value is 0.002 set.
Step 4: Decide whether or not to reject your null hypothesis
Based on the findings of your statistical test, you must decide whether to accept or reject your null hypothesis.
In most cases, you will base your decision on the p-value that the statistical test provides. When there is a less than 5% chance that these data would be observed if the null hypothesis were true, your predetermined level of significance for rejecting the null hypothesis will often be set at 0.05.
Other times, scientists will choose a lower level of significance, such 0.01 (1%). This lessens the likelihood of incorrectly rejecting the null hypothesis (Type I error).
An illustration of a hypothesis test
In your research of the difference in average height between men and women, you discover that the p-value of 0.002 is less than your threshold of 0.05, rejecting your null hypothesis that there is no difference.
Step 5: Share your findings
In the results and discussion portions of your research paper, dissertation, or thesis, you will provide the findings of hypothesis testing.
In the results section, you should include a concise analysis of the data as well as a summary of the outcomes of your statistical test (for instance, the estimated difference between group means and associated p-value). During the dialogue, you can discuss whether or not your initial idea was corroborated by your findings.
In the jargon of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You’ll probably need to do this for your statistics assignments.
A statistics assignment results from stating
We may reject the null hypothesis that males are not taller than women and come to the conclusion that there is probably a difference in height between men and women because our comparison of the mean heights of men and women revealed an average difference of 13.7 cm and a p-value of 0.002.
However, we rarely use this language when outlining study results in scholarly journals. Instead, we go back to our alternative hypothesis—in this case, that men are often taller than women—and say whether or not the test’s outcomes supported it.
In this case, the result is said to have “supported the alternate hypothesis.”
Adding findings to a research paper
With a p-value of 0.002, we found a 14.3 cm difference in average height between men and women, supporting our claim that there is a gender difference in height.
You can see that there are only slight differences between them; they both denote the same thing.