# Calculate The Test Statistic And P-Value That is, since the P -value, 0. Note that we would not reject H 0: The P -value for conducting the left-tailed test H 0: The P -value for conducting the two-tailed test H 0: That is, the two-tailed test requires taking into account the possibility that the test statistic could fall into either tail and hence the name "two-tailed" test.

## Hypothesis testing and p-values (video) | Khan Academy

Note that the P -value for a two-tailed test is always two times the P -value for either of the one-tailed tests. Now that we have reviewed the critical value and P -value approach procedures for each of three possible hypotheses, let's look at three new examples — one of a right-tailed test, one of a left-tailed test, and one of a two-tailed test. The good news is that, whenever possible, we will take advantage of the test statistics and P -values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

Specifically, the four steps involved in using the P -value approach to conducting any hypothesis test are: Specify the null and alternative hypotheses. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Using the known distribution of the test statistic, calculate the P -value: Right Tailed The P -value for conducting the right-tailed test H 0: Again, express these results as numbers. If we manipulate some experimental condition and the observed results differ from this expected results, two possibilities are possible: The purpose of finding a p-value is basically to determine whether the observed results differ from the expected results to such a degree that the "null hypothesis" - the hypothesis that there is no relationship between the experimental variable s and the observed results - is unlikely enough to reject Example: Let's say that, in our town, we randomly selected speeding tickets which were given to either red or blue cars.

We found that 90 tickets were for red cars and 60 were for blue cars. These differ from our expected results of and 50, respectively. Did our experimental manipulation in this case, changing the source of our data from a national one to a local one cause this change in results, or are our town's police as biased as the national average suggests, and we're just observing a chance variation?

### Statistics Online

A p value will help us determine this. Determine your experiment's degrees of freedom. Degrees of freedom are a measure the amount of variability involved in the research, which is determined by the number of categories you are examining. Our experiment has two categories of results: If we had compared red, blue, and green cars, we would have 2 degrees of freedom, and so on.

Compare expected results to observed results with chi square. Chi square written "x 2 " is a numerical value that measures the difference between an experiment's expected and observed values.

## P-Value in Statistical Hypothesis Tests: What is it?

The equation for chi square is: In other words, you'll need to calculate o-e -. In our example, we have two outcomes - either the car that received a ticket is red or blue. Our work would go as follows: Choose a significance level. Now that we know our experiment's degrees of freedom and our chi square value, there's just one last thing we need to do before we can find our p value - we need to decide on a significance level. Basically, the significance level is a measure of how certain we want to be about our results - low significance values correspond to a low probability that the experimental results happened by chance, and vice versa.

Significance levels are written as a decimal such as 0.

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This is NOT the case. By convention, scientists usually set the significance value for their experiments at 0. For most experiments, generating results that are that unlikely to be produced by a random sampling process is seen as "successfully" showing a correlation between the change in the experimental variable and the observed effect. For our red and blue car example, let's follow scientific convention and set our significance level at 0. Use a chi square distribution table to approximate your p-value.

Scientists and statisticians use large tables of values to calculate the p value for their experiment.

## Coming Soon

These tables are generally set up with the vertical axis on the left corresponding to degrees of freedom and the horizontal axis on the top corresponding to p-value. Use these tables by first finding your degrees of freedom, then reading that row across from the left to the right until you find the first value bigger than your chi square value. Look at the corresponding p value at the top of the column - your p value is between this value and the next-largest value the one immediately to the left of it.

Chi square distribution tables are available from a variety of sources - they can easily be found online or in science and statistics textbooks. If you don't have one handy, use the one in the photo above or a free online table, like the one provided by medcalc. Our chi-square was 3. So, let's use the chi square distribution table in the photo above to find an approximate p value. Since we know our experiment has only 1 degree of freedom, we'll start in the highest row.

### Video transcript

We'll go from left to right along this row until we find a value higher than 3 - our chi square value. The first one we encounter is 3. Looking to the top of this column, we see that the corresponding p value is 0.

Stats: Hypothesis Testing (P-value Method)

This means that our p value is between 0. Decide whether to reject or keep your null hypothesis. Since you have found an approximate p value for your experiment, you can decide whether or not to reject the null hypothesis of your experiment as a reminder, this is the hypothesis that the experimental variables you manipulated did not affect the results you observed.

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