In theory, we could also increase the significance level, but doing so would increase the likelihood of a type I error at the same time. We discuss these ideas further in a later module. In the long run, a fair coin lands heads up half of the time. For this reason, a weighted coin is not fair. We conducted a simulation in which each sample consists of 40 flips of a fair coin.
Here is a simulated sampling distribution for the proportion of heads in 2, samples. Results ranged from 0. In general, if the null hypothesis is true, the significance level gives the probability of making a type I error. This is a problem! Moore in Basic Practice of Statistics 4th ed. Freeman, :. This is an example of a probable type I error.
So the conclusion that this one type of cancer is related to cell phone use is probably just a result of random chance and not an indication of an association. Click here to see a fun cartoon that illustrates this same idea. Telepathy is the ability to read minds. Researchers used Zener cards in the early s for experimental research into telepathy. This is repeated 40 times, and the proportion of correct responses is recorded.
So in 40 tries, 8 correct guesses, a proportion of 0. But of course there will be variability even when someone is just guessing. Thirteen or more correct in 40 tries, a proportion of 0. When people perform this well on the telepathy test, we conclude their performance is not due to chance and take it as an indication of the ability to read minds.
These corresponding values in the population are called parameters. Imagine, for example, that a researcher measures the number of depressive symptoms exhibited by each of 50 adults with clinical depression and computes the mean number of symptoms.
The researcher probably wants to use this sample statistic the mean number of symptoms for the sample to draw conclusions about the corresponding population parameter the mean number of symptoms for adults with clinical depression. Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample.
The mean number of depressive symptoms might be 8. This random variability in a statistic from sample to sample is called sampling error. Note that the term error here refers to random variability and does not imply that anyone has made a mistake.
One implication of this is that when there is a statistical relationship in a sample, it is not always clear that there is a statistical relationship in the population. A small difference between two group means in a sample might indicate that there is a small difference between the two group means in the population.
But it could also be that there is no difference between the means in the population and that the difference in the sample is just a matter of sampling error. But it could also be that there is no relationship in the population and that the relationship in the sample is just a matter of sampling error. The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations. Null hypothesis testing is a formal approach to deciding between two interpretations of a statistical relationship in a sample.
This is the idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error.
This is the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population. Again, every statistical relationship in a sample can be interpreted in either of these two ways: It might have occurred by chance, or it might reflect a relationship in the population.
So researchers need a way to decide between them. Although there are many specific null hypothesis testing techniques, they are all based on the same general logic. The steps are as follows:. Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population.
We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population. A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. The researcher is claiming that 1 - p-value is the probability that the alternative hypothesis is false.
The p-value is not a probability of an alternative or null hypothesis being true or false. See the answer to part c. A pharmaceutical company trying to win approval for a new drug they manufacture claims that their drug is better than the standard drug at curing a certain disease.
The company bases this claim on a study in which they gave their drug to volunteers with the disease. They compared these volunteers to a group of hospital patients who were treated with the standard drug and whose information is obtained from existing hospital records.
The company found a "statistically significant" difference between the percentage of volunteers who were cured and the percentage of the comparison group who were cured. That is, they did a statistical hypothesis test and rejected the null hypothesis that the percentages are equal. As director of the F. Explain your reasoning in three or less sentences. Financial Ratios Guide to Financial Ratios. What Is a Null Hypothesis? Key Takeaways A null hypothesis is a type of conjecture used in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
The alternative hypothesis proposes that there is a difference. Hypothesis testing provides a method to reject a null hypothesis within a certain confidence level. Null hypotheses cannot be proven, though. Important Analysts look to reject the null hypothesis to rule out chance alone as an explanation for the phenomena of interest.
Compare Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. This compensation may impact how and where listings appear. Investopedia does not include all offers available in the marketplace. Related Terms How Hypothesis Testing Works Hypothesis testing is the process that an analyst uses to test a statistical hypothesis. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
What Is Alpha Risk? Alpha risk is the risk in a statistical test of rejecting a null hypothesis when it is actually true. Why Statistical Significance Matters Statistical significance refers to a result that is not likely to occur randomly but rather is likely to be attributable to a specific cause. What Is a Z-Test? A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. What P-Value Tells Us P-value is the level of marginal significance within a statistical hypothesis test, representing the probability of the occurrence of a given event.
Bonferroni Test Definition A Bonferroni Test is a type of multiple comparison test used in statistical analysis. Partner Links. Related Articles. Adjusted R-Squared: What's the Difference?
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