Hypothesis Testing

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

1. State your research hypothesis as a null (Ho) and alternate (Ha) hypothesis.
2. Collect data in a way designed to test the hypothesis.
3. Perform an appropriate statistical test.
4. Decide whether the null hypothesis is supported or refuted.
5. Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Understanding the Hypothesis:

As stated earlier there are two main components to hypothesis statements to be made, both completely different from each other.

Null Hypothesis: There is no relationship between A and B

Example: “There is no relationship between this flu medication and a reduced recovery time from the flu”.

The Null Hypothesis is usually denoted as: 𝐻0

Alternative Hypothesis: The hypothesis traditionally thought of when creating a hypothesis for an experiment

Example: “This flu medication reduces recovery time for the flu.”

The Alternative Hypothesis is usually denoted as: 𝐻1

Testing the Data:

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p-value. This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p-value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of data you collected.

P-Values:

p-value: The probability of observing a test statistic at least as large as the one observed, by random chance, assuming that the null hypothesis is true.

If you calculate a p-value and it comes out to 0.03, you can interpret this as saying “There is a 3% chance of obtaining the results I’m seeing when the null hypothesis is true.”

α (alpha value): The marginal threshold at which you’re okay with rejecting the null hypothesis.

An alpha value can be any value set between 0 and 1. However, the most common alpha value in science is 0.05.

When conducting an experiment, the process involves analyzing your p-value and comparing it against the alpha value.

p<α: Reject the Null Hypothesis and accept the Alternative Hypothesis

p>=α: Fail to reject the Null Hypothesis.

How you structure the test will determine what the p and α will be. The researcher has the option to select from a One-Tail or Two-Tail test.

1. One-tailed test, as the name suggests is the statistical hypothesis test, in which the alternative hypothesis has a single end. On the other hand, two-tailed test implies the hypothesis test; wherein the alternative hypothesis has dual ends.
2. In the one-tailed test, the alternative hypothesis is represented directionally. Conversely, the two-tailed test is a non-directional hypothesis test.
3. In a one-tailed test, the region of rejection is either on the left or right of the sampling distribution. On the contrary, the region of rejection is on both the sides of the sampling distribution.
4. A one-tailed test is used to ascertain if there is any relationship between variables in a single direction, i.e. left or right. As against this, the two-tailed test is used to identify whether or not there is any relationship between variables in either direction.

Example One-Tail Hypothesis

H1:μ1<μ2 The treatment group given this weight loss drug will lose more weight on average than the control group that was given a competitor’s weight loss drug

H0:μ1>=μ2 The treatment group given this weight loss drug will not lose more weight on average than the control group that was given a competitor’s weight loss drug”.

A Two-Tail Test is for when you want to test if a parameter falls between (or outside of) a range of two given values.

Example Two-Tail Hypothesis

H1:μ1≠μ2 “People in the experimental group that are administered this drug will not lose the same amount of weight as the people in the control group. They will be heavier or lighter”.

H0:μ1=μ2 “People in the experimental group that are administered this drug will lose the same amount of weight as the people in the control group.”

The results of the test determine whether or not the data compiled has significant resulants. Should the p value meet the threshold selects, the data is then ready to be presented showing that the findings are accurate and represent the population. On the other hand if the p-value is too high it indicates there is no correlation and a new variation of the study needs to be created to find the significant results. All this culminates to the base of developing research in an accurate and presentable setting.