Any statistical inference requires assumptions. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference. Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.
Whatever level of assumption is made, correctly calibrated inference in general requires these assumptions to be correct i. Incorrect assumptions of simple random sampling can invalidate statistical inference. More complex semi- and fully parametric assumptions are also cause for concern. The use of any parametric model is viewed skeptically by most experts in sampling human populations. In particular, a normal distribution would be a totally unrealistic and unwise assumption to make if we were dealing with any kind of economic population.
Here, the central limit theorem states that the distribution of the sample mean for very large samples is approximately normally distributed, if the distribution is not heavy tailed.
In statistical hypothesis testing, tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance; this can help to decide whether results contain enough information to cast doubt on conventional wisdom, given that conventional wisdom has been used to establish the null hypothesis.
The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. It is important to note the philosophical difference between accepting the null hypothesis and simply failing to reject it. Nonetheless, the terminology is prevalent throughout statistics, where its meaning is well understood. This fact expresses that our procedure is based on probabilistic considerations in the sense we accept that using another set of data could lead us to a different conclusion.
Rejection of the null hypothesis is a conclusion. We might accept the alternative hypothesis and the research hypothesis.
The evidence is insufficient to support a conclusion. This is like a jury that fails to reach a verdict. Whether rejection of the null hypothesis truly justifies acceptance of the research hypothesis depends on the structure of the hypotheses. Rejecting the hypothesis that a large paw print originated from a bear does not immediately prove the existence of Bigfoot. The two hypotheses in this case are not exhaustive; there are other possibilities. Maybe a moose made the footprints.
Hypothesis testing emphasizes the rejection which is based on a probability rather than the acceptance which requires extra steps of logic. Privacy Policy. Skip to main content. A Closer Look at Tests of Significance. Search for:. Was the Result Significant? Learning Objectives Assess the statistical significance of data for a null hypothesis. Key Takeaways Key Points In statistical testing, a result is deemed statistically significant if it is so extreme without external variables which would influence the correlation results of the test that such a result would be expected to arise simply by chance only in rare circumstances.
Key Terms statistical significance : A measure of how unlikely it is that a result has occurred by chance. We see some differences, but want to know if those differences are likely due to chance, because of the particular people we happened to interview, or whether the differences seen here likely reflect real differences in the entire population of people represented by our sample. To answer this question we used a statistic called chi pronounced kie like pie square shown at the bottom of the table in two rows of numbers.
The top row numbers of 0. The meaning of these statistics may be ignored for the purposes of this article. The second row contains values. These are the significance levels and are explained following the table. Significance levels show you how likely a pattern in your data is due to chance. The most common level, used to mean something is good enough to be believed, is.
However, this value is also used in a misleading way. Instead it will show you ". To find the significance level, subtract the number shown from one. For example, a value of ". In this table, there is probably no difference in purchases of gasoline X by people in the city center and the suburbs, because the probability is.
In contrast the high significance level for type of vehicle. The Survey System uses significance levels with several statistics.
In all cases, the p value tells you how likely something is to be not true. If a chi square test shows probability of. If a t-test reports a probability of. If a test shows a. If you do a large number of tests, falsely significant results are a problem. If you took a totally random, meaningless set of data and did significance tests, the odds are that five tests would be falsely reported significant. The common alpha values of 0. For a significance level of 0. The graphs show that when the null hypothesis is true, it is possible to obtain these unusual sample means for no reason other than random sampling error.
Significance levels and P values are important tools that help you quantify and control this type of error in a hypothesis test. Using these tools to decide when to reject the null hypothesis increases your chance of making the correct decision. If you like this post, you might want to read the other posts in this series that use the same graphical framework:. Minitab Blog. We'll use these tools to test the following hypotheses: Null hypothesis: The population mean equals the hypothesized mean Alternative hypothesis: The population mean differs from the hypothesized mean What Is the Significance Level Alpha?
What Are P values? Discussion about Statistically Significant Results A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. The significance level—how far out do we draw the line for the critical region? Our sample statistic—does it fall in the critical region? You Might Also Like. Statistics 6 Minute Read.
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