Confidence intervals and probability values are two important concepts in statistics. A confidence interval is a range of values that we estimate to be the true value.
A probability value is the estimate of how likely something is to happen. In this case, we say that there is a probability of .20 that someone will buy a product after viewing an ad. This means that out of every 100 people who see the ad, 20 will buy the product.
The problem with these two concepts is that they can be misinterpreted easily. People may think that if the confidence interval does not include the true value, then the hypothesis is not true. Or, they may think that if the probability does not reach 1, then it is not likely to happen. Both of these are incorrect!
This article will discuss how to correctly interpret confidence intervals and probability values.
Calculate P-value
Once you have Ho: P=.20 and Ha: P does not equal .20, and you have conducted a significance test, you can calculate the p-value.
The p-value is the probability of obtaining a test statistic at least as extreme as what you observed, or a more extreme one, if the null hypothesis is true.
In other words, if the null hypothesis is true (that the population proportion is .2), then there is a given probability of getting a sample proportion of .34 or higher. This probability is the p-value.
The lower the p-value, the less likely that the null hypothesis is true. Therefore, if your p-value is .001, then there is 1 chance out of 1,000 that the null hypothesis is true.
Describe the P-value
A P-value is the probability of obtaining a result as extreme as or more extreme than the actual result, assuming the hypothesis being tested is true.
In other words, it is the probability of rejecting the hypothesis when it is true. A low P-value indicates that the hypothesis is not likely to be true and that there is evidence against it.
A P-value of .20 means that there is a 20% chance that Ho: P=.20 is true and we would obtain a result as extreme as or more extreme than what we obtained in the sample, meaning we would fail to reject Ho.
Therefore, given a P-value of .20, one could not conclude that Ho: P does not equal .20 based on this sample. There is not enough evidence to reject Ho.
Know how to interpret the P-value
A P-value describes the probability of obtaining a result as extreme as the one you obtained or a more extreme one if the hypothesis is not true.
In other words, if the P-value is high, it means that the result you obtained would be unlikely if the hypothesis was true. On the other hand, if the P-value is low, it would be likely to obtain that result if the hypothesis was true.
There are thresholds for how high or low a P-value is significant. These thresholds vary based on what question you are asking and what field you are in. For example, in medical research, a P-value less than .05 is considered significant. This means that if you do a test 100 times, 5 of those times you would get a result as extreme as the one you obtained or more extreme if the hypothesis was not true.
It is important to note that just because your P-value is not below .05 does not mean that your result is not significant. It simply means that in order to conclude your results are not due to chance, your P-value must be below .05.
What is the significance of the P-value?
A P-value is the probability of obtaining a test statistic at least as extreme as the one that was obtained if the null hypothesis is true.
In other words, if the P-value is .05, then you can assume that there is only a 5% chance that the difference between the sample mean and population mean is this large or larger if the null hypothesis is true.
This means that there is a 95% chance that the difference between the sample mean and population mean is less than this number. This also means that you can reject the null hypothesis.
A P-value of .05 means that if Ho: p=.20 is true, then you will obtain a test statistic at least this large 2 out of 100 times due to random sampling error.
What is the conclusion?
In this case, the P-value is .028, which is less than the alpha value of .05. Therefore, we reject the null hypothesis that the mean weekly spending is equal to $20.
This means that we are fairly certain that the mean weekly spending is not equal to $20. We can say that there is a significant difference in spending between men and women!
Because this was such a clear difference in spending, we could even go so far as to say that women spend twice as much on average per week than men do. This would be a pretty extraordinary claim, but we can back it up with our data.
This also shows us how powerful testing and analyzing data can be.
Leave a Reply