# Statistical Decision Model and Statistical Tests

The accuracy of the research’s results depends on the statistical test chosen to measure variables. To decide what specific test to choose for the study, it is necessary to analyze the variables’ character. Considerations made during the decision process can be organized according to a series of questions to direct the process of choosing tests. The statistical decision model is necessary to direct the researcher’s decision-making process and to assist in choosing the appropriate approach to conduct the statistical analysis.

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## Decision Model and Explanation of Steps

 What is the number of IVs? What types and scales are used for IVs? What is the number of DVs? What types and scales are used for DVs? What are the characteristics of the sample? What is the purpose of the study? What test to choose? 1, 2 levels categorical nominal scale 1 numericalinterval, ratio scale sample size is < 30 differences between groups ttest 1, at least 3 levels categorical nominal scale 1 numericalinterval, ratio scale independent differences between group mean one-way ANOVA dependent repeated-measures one-way ANOVA 2, at least 2 or more levels categorical, nominal or ordinal scale 1 quantitative, interval, ratio scale independent Interaction, differences between combinations of IVs for DV two-way ANOVA independent and dependent mixed-design ANOVA 1, at least 2 levels categorical, nominal or ordinal scale 1 DV,1 covariate quantitative, interval, ratio scale independent differences between group mean ANCOVA 1, at least 2 levels categorical, nominal or ordinal scale 2 or more quantitative, interval, ratio scale independent MANOVA 1 or more categorical, nominal scale 1 categorical, ordinal scale 1 sample compare the data Chi-square test 1 categorical, nominal scale 1 numerical, ratio scale 1 or 2 samples differences between group mean Mann Whitney U test

To choose the statistical test, the researcher should focus on the information about variables, samples, and purpose of the study. The first step is the analysis of the presented variables: What number, types, and scales are used for IVs/DVs? These features are important to be noted because they are different for different tests. If researchers state that they have 1 categorical IV with 3 levels (the nominal scale), the use of the ANOVA is more appropriate than the use of t tests. To choose the test correctly, it is also necessary to discuss samples because the type of ANOVAs depends on the sample.

The final question about the purpose of the study will help to make the right decisions to test hypotheses. The model was created according to the algorithm, followed by researchers while discussing the study’s features. The most difficult part was to organize the algorithm in an understandable table to provide the answers to the main questions (APA, 2010, p. 112; MicrOsiris, n.d.). However, it was easy to fill in boxes with tests’ characteristics referring to the learned information.

## Research Studies

The first study of interest is the analysis of reading skills of students who were taught according to different techniques. Descriptive statistics: the highest median (SD = 5.24) was observed for Rapid Reading. The research question: Are there differences in the 2nd Grade students’ rate of reading depending on the technique? The hypotheses: H0: μ1 = μ2 = μ3, H0: There are no differences in students’ rate of reading depending on the reading technique. H1: μ1 ≠ μ2 ≠ μ3, H1: There are differences in students’ rate of reading depending on the reading technique. The IV is Reading Technique (3 categories: Traditional Reading, Rapid Reading, and Dynamic Reading) according to which students were taught to read. The IV is categorical, discrete, and measured according to the nominal scale. The DV is Rate of Reading measured in the number of words reading per minute. The DVs is quantitative and measured according to the interval scale.

The second study of interest is the analysis of the interaction between anxiety levels, gender, and family status. Descriptive statistics: the highest level of anxiety was observed in females (SD = 6.27) and in single persons (SD = 3.29). The research question: Do anxiety levels depend on gender and family status? The hypotheses: IV # 1, H0: μ1 = μ2, H0: There are no differences in females and males’ anxiety levels. H1: μ1 ≠ μ2, H1: There are differences in females and males’ anxiety levels. IV # 2, H0: μ1 = μ2, H0: There are no differences in anxiety levels of married and single persons. H1: μ1 ≠ μ2, H1: There are differences in anxiety levels of married and single persons. Interaction: H0: There is no interaction between anxiety levels, gender, and family status. H1: There is an interaction. The IVs are Gender (two categories: male and female) and Family Status (two categories: married and single); they are categorical, discrete, and measured according to the nominal scale. The DV is the Anxiety Level measured according to the anxiety scale from 0 to 100. The DV is discrete and quantitative, measured according to the interval scale.

## Using the Decision Model to Select Tests

To choose the appropriate test for the first study, it is necessary to focus on the variables’ number, type, and scale. There is 1 IV with three levels and 1 DV, the purpose is to discuss differences in means, and samples are independent. Thus, the appropriate test is selected with references to comparing the characteristics with those ones presented in the model, and this test is a one-way ANOVA. The second study differs from the first one in the number of IVs and the purpose which is to find the interaction between variables. Thus, the selected test is a two-way ANOVA. The tests were selected correctly, and the model is helpful to select the test while focusing on the variables, sample type, and purpose (Huck, 2012, p. 202). However, the model can be expanded to include more combinations and tests.

## Usefulness and Limitations of Decision Models

Statistical decisions models are useful for researchers because they provide algorithms of actions to perform while selecting tests. Having the model, researchers can choose the test which is most appropriate for the concrete sample and purpose because some designs are very similar, and differences in one aspect can matter. Limitations are in the fact that not all possible combinations of variables, samples, and purposes are presented in the model, and researchers can fail to find the answer to specific questions associated with their study (Trochim, 2006). Planning and development of the research design is a time-consuming and challenging process, and the model’s advantages are in saving time and resources to choose tests to make statistically correct measurements and scientifically correct conclusions.

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While creating and using the model, I have learnt how to organize the data and ask questions related to the study and why it is relevant to focus on the variables, samples, and purpose among other factors. I have reviewed all the learnt tests and succeeded in organizing them in a comprehensible model to make informed decisions while choosing tests. This model can be widely used for further researches because it guarantees the selection of the appropriate test among the actively used statistical analyses.

## Conclusion

Creation of a statistical decisions model is an important experience to reflect on different statistical tests and design a useful tool to utilize in the future career. Thus, the table is created appropriately to address the basic requirements to such a model.

## References

American Psychological Association (2010). Publication manual of the American Psychological Association (6th ed.). Washington, D.C.: American Psychological Association.

Huck, S. W. (2012). Reading statistics and research (6th ed.). Boston, MA: Pearson.

MicrOsiris (n.d.). The decision tree for statistics. Web.

Trochim, W. (2006). Selecting statistics. Web.

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