Mastering hypothesis testing: A beginner’s guide — theoretical knowledge

The field of statistics is usually divided into two baskets – descriptive and inferential statistics. Using methods and techniques of descriptive statistics, you get introduced to the dataset and its variables, their distribution, etc. With inferential statistics, you go more deeply into relationships between variables and make inferences – or decisions. One part of the inferential statistics which is used very often is hypothesis testing.

In this article, I will write about the basics of hypothesis testing, its key parts, and its underlying assumptions. This article will include theoretical knowledge only. If you are interested in practical knowledge (using R programming), please visit my blog to see the continuation of this article.

HYPOTHESIS TESTING – WHAT DOES IT STAND FOR?

Hypothesis testing is one of the most used statistical methods, mainly used to make decisions (inferences) about a population parameter based on a sample of data. Since it is not smart to research the whole population (mainly because of cost and time, but oftentimes because of availability of one), we research a small portion of that population (in order words, we sample it). Based on that sample and its statistics, we try to find out something about the population where the sample comes from.

Hypothesis testing is a method that helps us determine whether the evidence in a sample supports a specific hypothesis about a population.

KEY COMPONENTS OF HYPOTHESIS TESTING

There are a couple of components in hypothesis testing, like:

1. null hypothesis (H0) — it represents a statement of no effect, or status quo. It is the hypothesis that researchers typically go/test against.
   For example — the average weight of the population is 70 kilograms.
2. alternative hypothesis (H1, Ha) — it represents a statement of a change, it goes against the null hypothesis. That is a statement which researcher expects or wants to test for.
   For example — the average weight of the population is not 70 kilograms.
3. Test statistic — it is calculated from the sample data, and it is used to determine the likelihood of observing the sample data under the null hypothesis, or that the null hypothesis can’t be rejected. Usually, we use z-score or t-score (using t-test or z-test). The choice of which test we will use depends on the type of data, sample size, and the assumptions of each test. Common tests are t-test, z-test, chi-square test, and ANOVA.
4. Significance level (alpha) — it is the threshold or boundary for deciding whether to reject the null hypothesis. The most common alpha is 0.05, but 0.01 and 0.10 can also be used, depending on how sturdy the boundary has to be.
   Example — 0.05 means that there is 5% risk of rejecting the null hypothesis when it is true.
5. p-value — it is the value/probability of obtaining test results (gotten with the test statistics) as extreme as the observed results, which assumes that the null hypothesis can’t be rejected.
   For example — a p-value of 0.03 means that there is a 3% chance of observing the sample data if the null hypothesis is true.
6. decision rule — this rule puts together the p-value and significance level. Based on those two, a decision can be made whether we reject or fail to reject the null hypothesis.
   (CAUTION — you can never say that you accept the null hypothesis, you can only FAIL to reject it)
   For example — if the p-value is lower than alpha, you can reject the null hypothesis. If the p-value is higher or equal to alpha, you fail to reject the null hypothesis.

ASSUMPTIONS OF HYPOTHESIS TESTING

Before you can decide if your data is ready for hypothesis testing, you have to check the assumptions or prerequisites for test statistics used in the testing process. Two tests that are mostly used are z- and t-tests, so we will check the prerequisites for the t-test mainly:

1. independence — observations would have to be independent of each other. To check that, you would have to be introduced to the study design.
2. normality — the data should be approximately normally distributed. To check that, you can draw a boxplot and histogram to visualize the variables. Test-wise, you can use the Shapiro-Wilk test or additionally use the Q-Q plot.
3. homogeneity of variances — for two sample t-tests, the variances in the two groups should be equal, for the standard t-test. To check this, use Levene’s test or Bartlett’s test.

To know what are the exact steps in hypothesis testing and the next steps in these series, please visit my website to keep reading this article. This article is a part of Hypothesis testing series, where I will explain all parts of the testing, how to write code for it in R, and how to understand and explain findings of each tests. Stay tuned, as more is coming next week! In the meantime, don’t hesitate to contact me and visit my website for more materials, such as glossaries and cheat sheets for other areas.

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