What is the significance of a t statistic

Then you collect your data, plot the results, and calculate statistics, including the p-value, which incorporates variation and the sample size. If you get a p-value lower than your target, then you reject the null hypothesis in favor of the alternative.

Again, this means the probability is small that your results were due solely to chance. There is also a formula in Microsoft Excel and a number of other online tools that will calculate it for you. For example, if a manager runs a pricing study to understand how best to price a new product, he will calculate the statistical significance — with the help of an analyst, most likely — so that he knows whether the findings should affect the final price.

If the p-value comes in at 0. But what if the difference were only a few cents? But even if it had a significance level of 0. In this case, your decision probably will be based on other factors, such as the cost of implementing the new campaign. Closely related to the idea of a significance level is the notion of a confidence interval.

Say there are two candidates: A and B. Let's consider a study evaluating a new weight loss drug. Group A received the drug and lost an average of four kilograms kg in seven weeks.

Group B didn't receive the drug but still lost an average of one kg over the same period. Did the drug produce this three-kg difference in weight loss? Or could it be that Group A lost more weight simply by chance? Statistical testing starts off by assuming something impossible: that the two groups of people were exactly alike from the start. This means the average starting weight in each group was the same, and so were the proportions of lighter and heavier people.

Mathematical procedures are then used to examine differences in outcomes weight loss between the groups. They tell us how likely we would be to get differences between groups in our sample that are as large or larger than those we see, if there were no differences between the corresponding groups in the population represented by our sample.

In other words, these numbers tell us how likely is our data, given the assumption that there are no differences in the population. What we want to know is how likely there are differences in the population, given our data.

Logically, if we are sufficiently unlikely to get a difference found in our sample, if there were no difference in the population, then it is likely that there is a difference in the population. We used this logic in the first part of this article when we said that you can interpret significance numbers by considering 1-p as the probability that there is a difference in the population where p is the significance number produced by the program.

For example, if the significance level is. While this logic passes the common sense test, the mathematics behind statistical significance do not actually guarantee that 1-p gives the exact probability that there is a difference is the population. Even so, many researchers treat 1-p as that probability anyway for two reasons. One is that no one has devised a better general-purpose measure.

The other is that using this calculation will usually lead one to a useful interpretation of statistical significance numbers. In some non-survey fields of research, the possibility that 1-p is not the exact probability that there is a difference in the population may be more important. In these fields, the use of statistical significance numbers may be controversial. Go to Navigation Go to Content. Creative Research Systems. Get Your Free Consultation! This is the only product in our lineup that offers all features and tools we considered.

Develop and improve products. List of Partners vendors. Statistical significance refers to the claim that a result from data generated by testing or experimentation is not likely to occur randomly or by chance but is instead likely to be attributable to a specific cause.

Having statistical significance is important for academic disciplines or practitioners that rely heavily on analyzing data and research, such as economics, finance , investing , medicine, physics, and biology. Statistical significance can be considered strong or weak. When analyzing a data set and doing the necessary tests to discern whether one or more variables have an effect on an outcome, strong statistical significance helps support the fact that the results are real and not caused by luck or chance.

Simply stated, if a p-value is small then the result is considered more reliable. Problems arise in tests of statistical significance because researchers are usually working with samples of larger populations and not the populations themselves.

As a result, the samples must be representative of the population, so the data contained in the sample must not be biased in any way.

The calculation of statistical significance significance testing is subject to a certain degree of error. The researcher must define in advance the probability of a sampling error , which exists in any test that does not include the entire population. Sample size is an important component of statistical significance in that larger samples are less prone to flukes.

Only random, representative samples should be used in significance testing. The level at which one can accept whether an event is statistically significant is known as the significance level. Researchers use a test statistic known as the p-value to determine statistical significance: if the p-value falls below the significance level, then the result is statistically significant. The p-value is a function of the means and standard deviations of the data samples. The p-value indicates the probability under which the given statistical result occurred, assuming chance alone is responsible for the result.

If this probability is small, then the researcher can safely rule our chance as a cause. The p-value must fall under the significance level for the results to at least be considered statistically significant. The opposite of the significance level, calculated as 1 minus the significance level, is the confidence level.

It indicates the degree of confidence that the statistical result did not occur by chance or by sampling error. Statistical significance does not always indicate practical significance, meaning the results cannot be applied to real-world business situations.