P-value calculations: Understanding where the p-value comes from

Understanding where the p value comes from Hi, I’m, Dr Nic, and in this video I’m, going to tell you about where the p value comes from Before we start, please, like this video comment below subscribe, but most of all join the channel help. It to grow and help me help more and more people like you In other videos, I explain what the p value tells you and how to undertake a hypothesis test.

There are links to these videos in the description below In this video.

I’m going to work through an example to show you where the p value comes from and how you could calculate one for yourself.

The p value or sig can be found in the output to statistical inference.

You can have p values for testing if two means are different or if the slope of a line is statistically significant or if there is evidence of differences between categorical data.

All of the tests shown in the video Choosing which statistical test to use produce a p value.

Normally you just get a computer to find the p value You put in the data.

Tell a computer.

What you want to test for and out comes the p value.

However, it is good to have an understanding of what a p value actually is. A p value is a probability.

That is what the P stands for In SPSS.

It is called sig.

We want to know if an effect that shows up in a sample is evidence of an effect in the population from which the sample is drawn.

The p value tells us the probability that we would get the sample result by chance.

If there is no effect in the population, We will use a test for a population mean to illustrate this.

We will use the same example, as is shown in hypothesis test for a mean in Excel.

In this case, the orchard owner is comparing the mean weight of her apples with the export standard of a 152 grams per apple.

The orchard owner can see that the mean weight of the apples in the sample is about a 149 grams.

Could that just be by chance that the apples in the sample are mostly lighter than the ones in the whole orchard and in reality the average weight of the apples in the orchard is 152 grams or above We can use probability theory to work out? How likely it is to get a mean of a 149 grams or less if the mean weight of the apples in the population is 152 grams. This builds on the central limit theorem.

So you might like to watch that video now, if you’re not familiar with it, The central limit theorem talks about the nature of the sampling distribution of the mean If we were to take a whole lot of samples of size 15 from an orchard that Really did have a mean weight of 152 grams, we would get a variety of sample means.

This is known as the sampling distribution of the mean The mean of those sample means would be the same as the mean of the population.

The spread of the sample means is given as the standard error, the formula for which is sigma.

The population standard deviation over the square root of n the sample size.

The central limit theorem states that we can use a normal distribution to model the sampling distribution.

If we knew the population standard deviation, we could proceed from here.

However, we do not usually know the population standard.

Deviation, It’s actually pretty unlikely to know the population standard deviation.

When we do not know the population mean, but we do have a sample standard deviation, s which we can use as an approximation to the population standard deviation Sigma With small samples. We need to use the students T or T distribution instead of the normal distribution.

It is always okay to use the T distribution as it becomes the normal distribution for large samples.

The T distribution is like a standard, normal distribution.

It has a mean of 0 and a standard deviation of 1 To use the T distribution.

We need to find out how many standard errors the sample mean is from the hypothesized population mean We calculate the sample mean minus the hypothesized mean, and we find that it is 149 2667 152, which is 2 7333.

The standard error is 4 75795.

The sample standard deviation divided by the square root of 15, which gives 1 228497.

This is a measure of the spread of sample means.

We divide the distance that the sample mean is from the hypothesized mean by 1 228497, and we get 2 22494.

That is saying that the sample mean is a bit more than two standard errors below the hypothesized population mean Now we need to find out how likely that is in the appropriate T distribution. We use a T distribution with n minus 1 or 14 degrees of freedom Using Excel.

We use the function, t dist, 2, 22494, 14 true or we can use a calculator to find the probability.

The probability is 0 021519, which we will round to 0 022.

For the T, distribution with 14 degrees of freedom, the area under the graph to the left of 2 22494 is 0 022.

This is the p value we are looking for.

This p value tells us that if the population mean for all the apples in the orchard is 152 g, then the probability of getting a result – this much smaller than 152 or worse, is point 0 022.

About 2.

This video explained where a p value comes from.

There are links in the description to other videos to help you understand this concept and what you would do with the p value.

Now you’ve got it Even if you are not using Excel the video Hypothesis test for a mean in Excel will help you with your understanding, Do let me know what more you would like in the comments below Please like this video subscribe, but most of All join the channel, especially if you’re using our videos in your teaching, Help the channel grow and help me help more and more people like you, .

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