Hypothesis Testing: 3 Crucial Pillars in Statistics

Hypothesis testing revolves around determining whether a set of data can be supported by a particular hypothesis. Hypothesis testing uses statistical inference to deliver its outcomes. The method of testing enables us to provide probabilistic statements about different population parameters.

The Fundamentals of Hypothesis Testing

You will come across some known information while conducting any scientific research. The existing information can be in the form of a long-accepted idea, or it might also come from some other research in the past. Hypothesis testing is about determining whether the existing claims are true. Hypothesis testing revolves around the following:

  • Stating what we think is true
  • Using sample statistics to establish population parameter inferences
  • Quantifying how confident we feel about our claims

Use and Importance of Hypothesis Testing

Statistics are valuable for analyzing several data collections. It is also true in the case of hypothesis testing. It is useful for justifying conclusions even if there isn’t any scientific theory. Here are some real-world examples of hypothesis testing:

  • Determining whether more men suffer from a nightmare than women
  • Figuring out the effect of the full moon on behavior
  • Creating authorship of documents
  • Figuring out whether hospital carpeting leads to more infections
  • Evaluating the claims of handwriting analysts
  • Figuring out whether bumper stickers indicate car owner behavior
  • Choosing the best methods to stop smoking
  • Figuring out the range at which bats detect insects by echo

Statistical hypothesis testing has a huge impact on statistics and statistical inference. While reviewing the fundamental paper by Pearson and Neyman, Lehman spoke about the central role of several developments in the theory and practical application of statistics.

Significance testing is the preferred statistical tool in various experimental social sciences. Several other fields prefer the estimation of parameters. Significance testing has replaced traditional comparison of experimental results and predicted value.

Hypothesis Testing Components

The different components included within a proper hypothesis test are as follows:

Null Hypothesis:

It is a statement about a population parameter’s value, like the population proportion or means. The null hypothesis includes the condition of equality and is denoted using H-naught (H0).

Alternative Hypothesis:

It refers to the claim that’s being challenged and needs to be tested. The alternative hypothesis can be considered the opposite of the null hypothesis. It includes the parameter’s value that we consider practical. We denote the alternative hypothesis as H1.

Test Statistics:

It refers to the value calculated using sample data applied for making decisions regarding the rejection of the null hypothesis. On the basis of the notion that the null hypothesis is true, the test statistic can convert the sample mean or proportion into a z- or t-score. It helps understand whether there’s a significant claim difference between the hypothesized claim and the sample statistic.

P-Value:

It refers to the area under the curve to the right or left of the test statistic. The p-value is often compared to the level of significance.

Level of Significance:

It is the test statistic’s probability of falling into the critical region in a scenario with a true null hypothesis. The level of significance is always set by the researcher.

Conclusion:

It refers to the final decision of the hypothesis test. The conclusion always needs to be stated clearly. The conclusion also needs to communicate the decision according to the test components. While arriving at a conclusion, you must remember that the null hypothesis can neither be proved nor accepted. You can only say that the sample evidence isn’t adequate to reject the null hypothesis.

The conclusion includes two parts:

  • Rejecting or failing to reject the null hypothesis
  • There is or isn’t adequate evidence to back the alternative

Therefore, you have two options. You can either reject the null hypothesis or fail to reject it. When you reject the null hypothesis, it means that you have adequate statistical evidence to support the alternative claim. When you don’t have enough evidence to back the alternative claim, you won’t be able to reject the null hypothesis.

3 Pairs of the Null and Alternative Hypotheses

The null and alternative hypotheses include three different pairs, which are as follows:

A Two-Sided Test

This test helps determine whether the population parameter is equal to or not equal to some specific value. The critical region is usually segmented into two tails. The critical values usually define the rejection zones.

A Right-Sided Test

This test determines whether the population parameter is greater than equal to a specific value. The critical region stays in the right tail. The critical value will always be positive and remains in the rejection zone.

A Left-Sided Test

This test helps determine whether the population parameter is less than or equal to a particular value. The critical region is found in the left tail. The critical value will be negative and define the rejection zone.

A Popular Example of Hypothesis Testing

The Lady Tasting Tea is a well-known example of hypothesis testing. Dr. Muriel Bristol claimed that she could figure out whether the milk or the tea was added to a cup first. Fisher, the agricultural statistician and the one responsible for popularizing the significance test, gave eight cups to Dr. Muriel. Two varieties of cups were given, with four of each variety.
The cups were given to the lady in random order. According to the null hypothesis, the lady had no such abilities. The test statistic was quite straightforward and based on the success of selecting the four cups. The critical region included one case of 4 successes of 4 possible on the basis of conventional probability criterion.
A pattern of 4 successes can be in tune with 1 out of 70 possible combinations. Fisher declared that no alternative hypothesis was required. The lady accurately identified all the cups. It can be considered a significant result statistically.
When the observed results are unlikely under the notion that the null hypothesis is true, the result is considered statistically significant. When the result is statistically significant, we can reject the null hypothesis. The result is based on the level of significance, sample size, sample statistic, and the fact whether the alternative hypothesis is one-sided or two-sided.

Closing Thoughts

While testing, there can be two conclusions. At times, you reject the null hypothesis. At times, you might fail to reject it. Sometimes the conclusions are accurate, but at times, they can be inaccurate. Remember that inaccurate results can occur even after following all the right procedures.
Incomplete sample data is always used for arriving at a conclusion. Therefore, the possibility of reaching an inaccurate conclusion is always present. Hypothesis testing can provide four conclusions, two correct and two incorrect.

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