Inferential statistics provides scientists with a chance to make generalizations and draw conclusions without conducting too many experiments. It would be nearly impossible to survey every person on Earth, but representative sample surveys are manageable. However, the survey or experiment results do not draw a picture, and the data needs analysis to make sense.
For this reason, we use inferential methods to process the information, identify the probability distribution, and draw conclusions. Significance or hypothesis testing is one of the most common and essential techniques in your data science arsenal, so today we’ll cover its basics.
Statistical Hypothesis Testing
While the name of the technique sounds scary and complicated, it is not that difficult to understand. Statistical hypothesis testing is merely a way to tell whether your assumption was correct. For example, you may assume your data set has a normal distribution or that your two samples come from the same population distribution. To conduct the test, you need to understand two terms:
The null hypothesis (hypothesis 0 or H0) is the assumption of the statistical test. You assume your conclusion is correct or that nothing changes. Once you conduct the statistical testing, you can either reject the null hypothesis or fail to reject it. If the former is true, your initial assumption was wrong, and you have to consider other options, bringing us to
The alternative hypothesis (hypothesis 1, H1, or HA) is any other assumption aside from the initial one. It means that if your first conclusion was wrong; you need to look for other explanations of the data.
Hypothesis Testing Interpretation
Before you decide which hypothesis holds and draw conclusions, you need to conduct the test and interpret its results. Most common of them is the p-value. The value itself does not provide the grounds for rejecting either hypothesis until you compare it to a threshold value set before testing (significance level).
For social sciences, the significance level (alpha) is often set at 5% or 0.05. However, if you need a higher level of confidence, you can set alpha at 0.01 or 1%. When you compare p-value to alpha, there are two possible options:
P-value is greater than alpha. This means the results are not significant, your initial assumption was wrong, and the null hypothesis is rejected.
P-value is equal or less than alpha. This means your results are significant, the null hypothesis fails to be rejected, and your initial assumption was correct.
When presenting results of the hypothesis testing, always include the significance level or the confidence level. The latter can be calculated by subtracting the significance level from 100%. If your significance level is 5%, the confidence level is 95%.
However sure you are of your results, keep in mind their probabilistic nature. With inferential statistics, your confidence level can never be 100%, meaning your null hypothesis is never true or false. It is merely rejected or fails to be rejected at a certain significance level. Even if your initial assumption (H0) is accepted, there is still a chance of it being wrong.
Correct hypothesis testing procedures and their results interpretation are a complicated, yet crucial part of data science irrelevant to the field of study. Considering the number of possible mistakes and misinterpretations, it’s no wonder many people do not trust statistical results. However, it is in your best interest to learn the proper hypothesis testing methods to ensure your research in school and work results after graduation are taken seriously.
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