Before we understand what ANOVA is, we need to first understand specific concepts such as the mean, sample, parameter, statistics, and population (Back, 2017). Mean is obtained by summing all the data entries in a population or a sample and then dividing the total summation by the total number of data entries. The mean is referred to as the average score of a population or sample (Mickey, Dunn, & Clark, 2010). Mean is one of the characteristics of a population or a sample that can be measured as described above.
Any measurable characteristic of a sample is referred to as a statistic. Any measurable characteristic of a population is referred to as a parameter.
Population refers any group of individuals or items that are subjects of a study (Back, 2017). For example, we can talk of a population of fifty in a class of fifty students. We can also talk of a population of 20 in a group of 20 cars and so on. If the students are given an exam and their mean average ought to be determined, we add all their scores and divide by their total number/population which is 50.
We can have as many populations as possible depending on the type of study to be conducted. For example, in a school, we can have ten classes each with a population of 50 students. In case the students take an exam, each class will have its average score. This means that we can have ten mean average scores for the ten classes, in statistical analysis each class is referred to as a population.
The means obtained from different population vary significantly. In this regard, statisticians would like to know to what extent do the means vary. The variation between the means is what is referred to as the differences of means (Back, 2017). These differences are determined by the use of a special statistic method called the analysis of variance.
The populations can be subdivided into smaller units called samples. A sample consists of one or more observations from a population.
The analysis of variance is popularly referred to as ANOVA. It is a statistical method that is used when testing the difference between two or more means. We do not call it the analysis of means. The rationale behind this is that the inferences about mechanisms are made based on variance. The use of ANOVA tests the general differences between mean and not the specific differences. The populations or samples are sometimes referred to as groupings (Scheffé, 2010). These groups have varying features. Different parameters and statistic explain the features
ANOVA tells you if a set of features lessens the amount of unexplained information more by having the groupings than by forgetting all groupings. There are times when you are better off dropping features.
At the point when just two samples are taken a gander at, the t-test and ANOVA test will yield similar results.
Past two illustrations, the t-test can be utilized to evaluate other means utilizing numerous t-tests, but this method winds up noticeably problematic and subject to error (Scheffé, 2010).
We can do it today.
ANOVA or investigation of variance enables one to utilize statistics to test the contrasts between at least two means and reduces the probability for a type 1 error, which might happen when taking a gander at multiple two-sample t-tests (“10. Alternatives to analysis of variance). Therefore, ANOVA is used for testing hypotheses where there are multiple means or populations.
A hypothesis is a statement or proposed explanation that is done with less evidence to support its validity. Type 1 error occurs when you take the hypothesis to be false when it is true (Scheffé, 2010). Accepting a false hypothesis results to what is called type two error.
- Alternatives to analysis of variance. (n.d.). Statistics in Language Research. doi:10.1515/9783110877809.211
- Back, K. E. (2017). Mean-Variance Analysis. Oxford Scholarship Online. doi:10.1093/acprof:oso/9780190241148.003.0005
- Mickey, R. M., Dunn, O. J., & Clark, V. (2010). Applied statistics: Analysis of variance and regression. Hoboken, NJ: Wiley-Interscience.
- Scheffé, H. (2010). The analysis of variance. New York: Wiley-Interscience Publication.