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.
What is statistical significance anyway? We want to determine whether our sample mean I left you with a question: where do we draw the line for statistical significance on the graph? Now we'll add in the significance level and the P value, which are the decision-making tools we'll need.
For example, a significance level of 0. These types of definitions can be hard to understand because of their technical nature. A picture makes the concepts much easier to comprehend! The significance level determines how far out from the null hypothesis value we'll draw that line on the graph. To graph a significance level of 0. In the graph above, the two shaded areas are equidistant from the null hypothesis value and each area has a probability of 0. In statistics, we call these shaded areas the critical region for a two-tailed test.
The critical region defines how far away our sample statistic must be from the null hypothesis value before we can say it is unusual enough to reject the null hypothesis.
Our sample mean The sample mean is The absolute deviation from the average is This means that there is a Since this probability is large, we conclude that the null hypothesis is true. What if the p-value was small, like 0. 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. In this situation, we would gladly accept a greater value for alpha if it resulted in a tradeoff of a lower likelihood of a false negative.
A level of significance is a value that we set to determine statistical significance. This ends up being the standard by which we measure the calculated p-value of our test statistic. To say that a result is statistically significant at the level alpha just means that the p-value is less than alpha. There are some instances in which we would need a very small p-value to reject a null hypothesis. If our null hypothesis concerns something that is widely accepted as true, then there must be a high degree of evidence in favor of rejecting the null hypothesis.
This is provided by a p-value that is much smaller than the commonly used values for alpha. There is not one value of alpha that determines statistical significance. Although numbers such as 0. As with many things in statistics, we must think before we calculate and above all use common sense.
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