Article Sources. Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy. 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. T-Test Definition A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. What Does Statistics Study? Statistics is the collection, description, analysis, and inference of conclusions from quantitative data.
Partner Links. Related Articles. Investopedia is part of the Dotdash publishing family. Your Privacy Rights. To change or withdraw your consent choices for Investopedia. At any time, you can update your settings through the "EU Privacy" link at the bottom of any page. Published on March 6, by Rebecca Bevans. Revised on January 7, ANOVA, which stands for Analysis of Variance, is a statistical test used to analyze the difference between the means of more than two groups.
Use a one-way ANOVA when you have collected data about one categorical independent variable and one quantitative dependent variable. The independent variable should have at least three levels i. ANOVA tells you if the dependent variable changes according to the level of the independent variable. For example:. The alternate hypothesis H a is that at least one group differs significantly from the overall mean of the dependent variable. If you only want to compare two groups, use a t-test instead.
ANOVA determines whether the groups created by the levels of the independent variable are statistically different by calculating whether the means of the treatment levels are different from the overall mean of the dependent variable. If any of the group means is significantly different from the overall mean, then the null hypothesis is rejected. This allows for comparison of multiple means at once, because the error is calculated for the whole set of comparisons rather than for each individual two-way comparison which would happen with a t-test.
The F-test compares the variance in each group mean from the overall group variance. In addition to reporting the results of the statistical test of hypothesis i. In this example, participants in the low calorie diet lost an average of 6. Participants in the control group lost an average of 1. Are the observed weight losses clinically meaningful? Calcium is an essential mineral that regulates the heart, is important for blood clotting and for building healthy bones.
While calcium is contained in some foods, most adults do not get enough calcium in their diets and take supplements. Unfortunately some of the supplements have side effects such as gastric distress, making them difficult for some patients to take on a regular basis. A study is designed to test whether there is a difference in mean daily calcium intake in adults with normal bone density, adults with osteopenia a low bone density which may lead to osteoporosis and adults with osteoporosis.
Adults 60 years of age with normal bone density, osteopenia and osteoporosis are selected at random from hospital records and invited to participate in the study. Each participant's daily calcium intake is measured based on reported food intake and supplements. The data are shown below. Normal Bone Density. Is there a statistically significant difference in mean calcium intake in patients with normal bone density as compared to patients with osteopenia and osteoporosis?
In order to compute the sums of squares we must first compute the sample means for each group and the overall mean. For the participants with normal bone density:. X - We do not reject H 0 because 1. Are the differences in mean calcium intake clinically meaningful? If so, what might account for the lack of statistical significance?
The video below by Mike Marin demonstrates how to perform analysis of variance in R. It also covers some other statistical issues, but the initial part of the video will be useful to you. The factor might represent different diets, different classifications of risk for disease e. There are situations where it may be of interest to compare means of a continuous outcome across two or more factors. For example, suppose a clinical trial is designed to compare five different treatments for joint pain in patients with osteoarthritis.
Investigators might also hypothesize that there are differences in the outcome by sex. This is an example of a two-factor ANOVA where the factors are treatment with 5 levels and sex with 2 levels. In the two-factor ANOVA, investigators can assess whether there are differences in means due to the treatment, by sex or whether there is a difference in outcomes by the combination or interaction of treatment and sex.
The following example illustrates the approach. Consider the clinical trial outlined above in which three competing treatments for joint pain are compared in terms of their mean time to pain relief in patients with osteoarthritis.
Because investigators hypothesize that there may be a difference in time to pain relief in men versus women, they randomly assign 15 participating men to one of the three competing treatments and randomly assign 15 participating women to one of the three competing treatments i. Participating men and women do not know to which treatment they are assigned.
They are instructed to take the assigned medication when they experience joint pain and to record the time, in minutes, until the pain subsides. The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:.
If, however, the one-way ANOVA returns a statistically significant result, we accept the alternative hypothesis H A , which is that there are at least two group means that are statistically significantly different from each other. At this point, it is important to realize that the one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were statistically significantly different from each other, only that at least two groups were.
0コメント