# Processing of the results of intergroup experiments...

## Processing of the results of intergroup experiments

The general scheme for performing a statistical analysis of a two-level intergroup experiment corresponds to the scheme described above for intrasubject plans, except that other statistical criteria are used to compare the indicators.

The choice of the type of statistical criterion is determined by the way in which the equivalent groups were created in the study.

If you used random distribution or clustering, then for comparison, you should apply the criteria for unrelated samples. This is a parametric Student's t-criterion for unrelated samples (if the compared data are distributed according to the law of normal distribution and there is homogeneity of the variance for both groups) or its nonparametric analog - the Mann-Whitney test (if the data do not correspond to the law of normal distribution or the dependent variable measured in the ordinal scale).

Mathematically, the structural model of the intergroup two-level plan can be represented as the following equation:

where m j is the theoretically expected value of the dependent variable in the ideal experiment at j independent variable whose effect is

is investigated in a real experiment; ε ij - the experimental error for the i-th subject at j -th level independent variable, representing the effect of the side variables (theoretically, the zero value of this parameter is expected). It is assumed that the value of the dependent variable Xu, changed during the experiment, is the result of the addition of these two parameters.

The differences between the two averages can be expressed as follows:

Therefore, the differences between empirically averages can be explained by differences in theoretical averages, i.e. the effect of the independent variable and the differences in the mean values ​​of the experimental error, which is the effect of the uncontrolled spin-off variables. Therefore, the problem of statistical analysis is to estimate the experimental differences between the mean values ​​in the two groups relative to the magnitude of the experimental error.

Using the Student's test is based on the assumption that the effects of the dependent variable are independent of the effects of the side variables. In other words, the homogeneity of the variance of the dependent variable is assumed. Combining variances in two groups, we build the statistics t

Here n and m - the number of subjects in each group (as a rule, in the experiment these values ​​are equalized ). The value of S total is an estimate of the total variance in two experimental conditions. It can be calculated using the following formula:

The very assumption of homogeneity of the variance requires statistical verification. As a rule, Livin's test is used for this.

If the assumptions about the normality of the distribution of the dependent variable and the homogeneity of the variances are true, the given statistics t is described by the Student's t-distribution with n + n - 2 degrees of freedom.

Theoretical studies show that Student's test is not very sensitive to its basic assumptions, and therefore it is generally recommended to use it. However, if the values ​​of the dependent variable obtained in the experiment represent the results of the ranking, it would be useful to use nonparametric statistics.

If an equalization procedure was carried out and each subject in one group was selected as a pair for the subject in the other group on the basis of the parameters of the monitored parameter, the obtained values ​​of the dependent variable in the two groups turn out to be statistically connected. In this case, it is necessary to use the same criteria that are used in processing the results of intra-subject experiments: the t-Student's parametric test for coupled samples or the non-parametric Wilcoxon test.

When presenting the results in a scientific report, it is necessary to provide descriptive statistics for the dependent variable in each condition (mean and standard deviation), indicate by what criterion the comparison was made, to bring the value of the criterion and its p-level.

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