What is alpha in statistics

We would reject the null hypothesis. Another way of looking at the p-value is to examine the z value for the sample average. Remember that a z value measures how far, in standard deviations, a value is from the average. The z value for a sample average is given below. So, the sample average of The probability of getting z is the p-value of 0.

How does the p-value vary with random samples over time? It turns out it varies much more than you would think. The p-values were calculated for each those random samples with 20 observations shown in Figure 2. The maximum p-value was 0. The minimum p-value was 0. That is a large range when taking 20 random observations from the same population. The distribution of the p-values is shown in Figure 3.

Figure 3: Distribution the p-value for Random Samples. The chart almost looks like a uniform distribution. In this case, it is.

With continuous data and assuming the null hypothesis is true, the p-values are distributed uniformly between 0 and 1. Remember, a p-value measures the probability of getting a result that is at least extreme as the one we have — assuming the null hypothesis is true.

It does not measure the probability that the hypothesis is true. Nor does it measure the probability of rejecting the null hypothesis when it is true.

That is what alpha does. So, how do we use these two terms together. Basically, you decide on a value for alpha. What probability of being wrong do you want to use? What makes you comfortable? You then collect the data and calculate the p-value. If the p-value is greater than alpha, you assume that the null hypothesis is true. If the p-value is less than alpha, you assume that null hypothesis is false. What do you do if the two values are very close?

For example, maybe the p-value is 0. It is your call to make in those cases. You can always choose to collect more data. Note that the confidence interval and p-value will always go to the same conclusion. If the p-value is less than alpha, then the confidence interval will not contain the hypothesized mean. If the p-value is greater than alpha, the confidence interval will contain the hypothesized mean.

This publication examined how to interpret alpha and the p-value. Alpha, the significance level, is the probability that you will make the mistake of rejecting the null hypothesis when in fact it is true. The p-value measures the probability of getting a more extreme value than the one you got from the experiment. If the p-value is greater than alpha, you accept the null hypothesis. If it is less than alpha, you reject the null hypothesis.

Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position. When you wrote "This means that there is a The probability of a mean of You are correct as usual.

I should have applied it to the upper portion of the distibution only once you know what the sample aveage is. I revised the wording to reflect your comments. Wow, thanks for your super clear explanation! To avoid making a Type II error, we would usually say that we "fail to reject the H0" or "do not reject the H0. You said it better earlier in the page, but it is still best to say "The p-value measures the probability of getting a more extreme value than the one you got from the experiment assuming the null is true.

Is the a better way to conclude when the P value is less than or equal to the alpha in a meaningful way to the average educator like a teacher? Not sure what you mean, but I think Figure 1 makes it clear if there is a significant difference or not - good visual picture.

This was a well written and thorough explanation of both concepts. Thank you so much!! To make life easier, run only one experiment with enough sample size determined by pre-chosen statistical power and make only one conclusion.

You cannot fully explain the nature of statistical tests without mentioning probabilty of type 2 error "beta", which tells about statistical power. Collecting more of the same data is not p-hacking i don't believe.

My understanding of p-hacking is that you perform many statistical tests on the data and only report those that come back with significant results. These values are used to determine how meaningful the results of the test are. Alpha is also known as the level of significance. This represents the probability of obtaining your results due to chance. Alpha also represents your chance of making a Type I Error. The chance that you reject the null hypothesis when in reality you should fail to reject the null hypothesis.

In other words, your sample data indicates that there is a difference when in reality, there is not. Like a false positive. The other key-value relates to the power of your study. It logically follows that the greater the power, the more meaningful your results are.

Beta also represents the chance of making a Type II Error. With a Type II Error, you incorrectly fail to reject the null. In simpler terms, the data indicates that there is not a significant difference when in reality there is.

We can also see if it is statistically significant using the other common significance level of 0. The two shaded areas each have a probability of 0. This time our sample mean does not fall within the critical region and we fail to reject the null hypothesis.

This comparison shows why you need to choose your significance level before you begin your study. It protects you from choosing a significance level because it conveniently gives you significant results! Thanks to the graph, we were able to determine that our results are statistically significant at the 0. P-values are the probability of obtaining an effect at least as extreme as the one in your sample data, assuming the truth of the null hypothesis.

This definition of P values, while technically correct, is a bit convoluted. To graph the P value for our example data set, we need to determine the distance between the sample mean and the null hypothesis value In the graph above, the two shaded areas each have a probability of 0.

This probability represents the likelihood of obtaining a sample mean that is at least as extreme as our sample mean in both tails of the distribution if the population mean is When a P value is less than or equal to the significance level, you reject the null hypothesis. If we take the P value for our example and compare it to the common significance levels, it matches the previous graphical results. The P value of 0. If we stick to a significance level of 0. A common mistake is to interpret the P-value as the probability that the null hypothesis is true.

To understand why this interpretation is incorrect, please read my blog post How to Correctly Interpret P Values.