What Is a Null Hypothesis?

A null hypothesis🐼 is a foundational concept in statistics that assumes there is no real relationship or effect in the data being analyzed, and that any variations or trends are simply the result of random🌼 fluctuation rather than a true underlying cause.

澳洲幸运5开奖号码历史查询:Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the “null,” it is represented as H₀.

The null hypothesis, also known as “the conjecture,” is used in 澳洲幸运5开奖号码历史查询:quantitative analysis to test the𓆏ories about markets, investing strategies, and economies to decide if an idea is true or false.

Understanding a Null Hypothesis

A gambler may be interested in whether a game of chance is fair. If it is, then the expected earnings per play come to zero for both players. If it is not, then th⛄e expected earnings are positive for one player and negative for the other.

To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, and then tests the nul💙l hypothesis that the expected earnings are not different from zero.

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the 澳洲幸运5开奖号码历史查询:sample data are near zero, the🎃n the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and zero is explainable by chance a🌸lone.

The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the꧒ data and zero is due to chance.

Analysts look to reject the null hypothesis because doing so is a strong conclusion. This requires evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that while factors ཧother than chance may be at work, they may not be strong enough for the statistical test to detect them.

The Alternative Hypothesis

An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H₁).

For the examples bel♑ow, the alternative hypothesis would be:

• Students score an average that is not equal to seven.
• The mean annual return of a mutual fund is not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothe♍s❀is.

Null Hypothesis Examples

Here is a simple example: A school principal claims that students in their school score an average of seven out of 10 in exams. The null hypothesis is that the population mean is not 7.0. To test this null hypothesis, we record marks of, say, 30 students (sample) from the entire student population of th🧸e school (say, 300) and calcu🍬late the mean of that sample.

We can then compare the (calculated) sample mean to the (hypothesized) population mean of 7.0 and attempt to reject the null hypothesis. (The ♈null hypothesis here—that the population mean is not 7.0—cannot be proved using the sampl🦋e data. It can only be rejected.)

Take another example: The annual return of a particular 澳洲幸运5开奖号码历史查询:mutual fund is claimed to be 8%. Assume that the mutual fund has been in existence for 20 years. The null hypothesis is that the mean return is not 8% for the mutual fund. We take a random sample of 澳洲幸运5开奖号码历史查询:annual returns of the mutual fund for,♔ say, five years (sample) and calculat😼e the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.

For the above examples,ꦬ the null hypotheses are:

• Example A: Students in the school don’t score an average of seven out of 10 in exams.
• Example B: The mean annual return of the mutual fund is not 8% per year.

For the purposes of determining whether to reject the null hypothesis (abbreviated H0), said hypothesis is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average sco🎐re on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean i♌s 7.0).

If the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be “explainable by chance alone,” being within the range that is determined by chance alone.

How Null Hypothesis Testing Is Used in 𝔉Investments

As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock. The null hypothesis states that there is🅰 ꦕno difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.

Refuting the null hypothesis would require showing 澳洲幸运5开奖号码历史查询:statistical significance, which can be found by a🌄 variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return 🧔than a traditional buy-and-hold strategy.

One tool that can determine the statistical significance of the results is the p-value. A p-value represents the probability that a difference as large🌟 or larger than the observed difference between the two𓆏 average returns could occur solely by chance.

A p-value that is less than or equal to 0.05 often indicates whether there is evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns (the p-value is less than or equal to 0.05), she can then reje⛄ct the null hypothesis and conclude the alternative hypothesis.

The Bottom Line

A null hypothesis states there is no difference between groups or a relationship between variables. It is a type of statistical hypothesis and proposes that no statistical significance🐭 exists in a set of given observations. “Null” means nothing.

The null hypothesis is used in quantitative analysis to test theories about economies, investing strategies, and markets to decide if an idea is true or false. Hypothesis testing assesses the credibility of a hypothesis by using sample data. It is represented as H₀ and is sometimes simply known as “the null.”

Correction—July 23, 2024: This article was corrected to state accurate examples of the null hypothesis.