# This is stronger than average (One-Sample T Test)

One-Sample T Test. Usually, if we encounter data, we rush to find out the average of the data set. The goal is none other than to find the middle value. In fact, the average does not necessarily reflect the middle value of the data distribution that we encounter. The most concrete example is Indonesia’s per capita income. Although the per capita income is far from the poverty rate, due to the unequal distribution of wealth, the income does not reflect the real income received by each Indonesian citizen. In fact, I once read that the wealth of four people in Indonesia equals the wealth of millions of people in Indonesia.

Back to the topic: so what is stronger than average? We can find the average value, but if we want to use the average value to describe the research results, then we must first test the average value to see whether it is significant or not. If the average value is significant, then we can use the average value to complete the research objectives.

For example? A case example: we count the number of rice panicles. We have some data from field observations. We have a standard that the number of rice panicles should reach 20 panicles per tree. Then how do we guarantee that our observation data reaches the predetermined standard? If that is the case, then you can use the one-sample t test.

## Requirements that the one-sample T test must fulfill

This one-sample T test has requirements that must be met. This test is included in parametric testing, so

1. The sample used must come from a normally distributed population.
2. The type of data is quantitative.
3. The number of populations or samples used is at least 30.

Here is an example of the data that I will process in this article:

I made two columns because of screen limitations. The picture explains that the average number of panicles is 22. Is it really significant that it has met the standard of 20 panicles? Let’s prove it together. Remember, never say that this average result has met the standard before we do a statistical test, let alone say it in a seminar. Maybe it would be understandable if you are a high school student.

Let’s open the statistics application. This time, I used Minitab 17. I used Minitab because it is light and simple enough for this test.

We enter the data we want to test, then click stat – basic statistic – 1-sample t in minitab.

In the second column (the larger one), we click, and on the left side, a variable will appear. Double-click the variable panicle to enter the box. Check and perform a hypothesis test. And give a value of 20 (the standard value in this exercise example) in the hypothesized mean.

Click the option, and then a window will appear. We fill in the conviction level value, for example, 95 (meaning we want to know the significant level with α ≤ 0.05). Then, below, we can choose the hypothesis we will use. Whether using the hypothesis that the mean is not equal, greater, or less than the hypothesized mean This time, I use a mean greater than the hypothesized mean. Then click OK.

You can also add graphics if needed by clicking the option button. Then click OK to wait for the process to complete.

It can be seen that the t value is 3.7 and significant with a p-value of 0.000. The p-value is still below the limit or confidence level with α = 0.05. So it can be concluded that we accept H1, which means accepting the hypothesis that the average value is> 20. You can also try other hypotheses, for example, smaller or not equal to the standard or target value, to confirm the results. I did the same and got the following results:

From our three efforts, we can conclude that the average is significant with a value of 0.05 that:

average value > 20. significant at α value = 0.000
average value = 20. significant at α value = 0.001
average value of 20. significant at α value = 1.000 (not significant)

we could have said average value = 20, because this statement is still significant at α < 0.05. but we cannot say average value < 20, because the value is significant at α > 0.05.

You can use harvest data, or plant height, or number of seeds, pest attack, and others according to the data you have. This hypothesis test can help you to further describe the research results. And don’t forget that the data used is parametric.

The T test is part of the univariate, or one free sample case. You can read other statistical techniques that are still included in univariate in the article: Case of one free sample.

Thank you.