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## Key Steps in Mixed Model Data Analysis

Question:

Describe about the main ideas of Quantitative and Qualitative Mixed Models data Analysis methods?

Literature review and ANOVA

Mixed model data analysis is consist with the two main important analysis processes such as qualitative data analysis and quantitative data analysis. When we get the output for an experiment as a number or quantity, then we use the quantitative data analysis. There are several data analysis process or methods are available for quantitative data set. We can perform descriptive statistical analysis or inferential statistical analysis which is depends on our research question. Sometimes, we get the qualitative data for some experiments and for this qualitative data; we cannot use all the methods which are useful for the quantitative data analysis. We use other statistical data analysis methods for the qualitative data analysis. There are several data analysis methods are available for the qualitative data analysis. For some experiment, we have available both types of data, that is, experiment produces qualitative and quantitative data at the same time, then we need to use the both types of data analysis methods, this types of data analysis is called as the mixed models data analysis. In the mixed model data analysis, the primary step is to identify the variables for which we want to study or analyse the data regarding some particular variables. To decide or fix our goal or aim is very important in the mixed model data analysis. For the both qualitative and quantitative data analysis, collection of data is very important step for further research. Without data we cannot draw the conclusions regarding our hypothesis or claims regarding the different variables under study. Collection of data consist of several methods, we can use different sampling methods for collection of data. it was found that if we get the big sample, then we get more accurate results. Also, collection of data in the systematic format is very important. It is very useful to divide the data according to different categories. Sometimes, in the qualitative data analysis, we are not given any categories or label, then we need to divide the variable according to categories, label to these categories and coding is also important in the qualitative data analysis process. After collection of data, for the quantitative data analysis, we simply apply the different descriptive statistical methods and inferential statistical methods. We can calculate the different values for parametric estimation or descriptive statistics. We can use the non-parametric methods sometimes. For the qualitative data analysis, we can apply different qualitative data analysis methods and then we can calculate the desirable statistic value for proving our goals or aims regarding the hypothesis or claims stated by researcher. After both types of data analysis, we can draw the conclusions for given variables or claims regarding the variables under study.

In the descriptive statistics, we study the mean, mode, median, minimum, maximum, standard deviation, variance, range, skewness, kurtosis etc. There are lot of statistical software’s. We can use these software’s for getting the descriptive statistics values for the further analysis. In the inferential statistics, we apply the different statistical hypothesis tests for the given data. Selection of the proper test is very important in proving the claim or hypothesis under study. If we select the improper statistical tests, then we cannot get the correct conclusions. There are so many hypothesis tests are available and after checking all assumptions for using any particular test, we can apply this test to the given data and we can draw the conclusions for the given hypothesis stated for the test. After deciding the appropriate test, it is important to establish the null and alternative hypothesis for this test. This is nothing but the deciding our claim regarding the variable under study. After deciding our claim, we have to fix some level of significance or alpha value for the test. This is important because it gives us reliability or accuracy about the results of the test. In most of the times we take the level of significance as 5% or 0.05. Next step in the testing of hypothesis is to find the test statistic value and we can find this test statistic value by calculating the given formula for the test statistic. After finding the value for the test statistic value, we can find the p-value for the given value by using some statistical tables. Then we compare this p-value with the given level of significance or alpha value and then we take the decision regarding the null hypothesis according to the decision rule for the rejecting or not rejecting the null hypothesis. The decision rule for the rejecting or not rejecting the null hypothesis is given as below:

## Descriptive Statistics and Inferential Statistics

Decision rule: We reject the null hypothesis if the p-value is the less than the given level of significance or alpha value and we do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value.

Now, we have to see what is the ANOVA is. If we are given the two samples for testing the averages or means regarding the population data, then we can use the t test or z test. We can only use the z or t test when there are two samples. But many times, we need to compare more than two samples for the population means or averages for the given data set. In this condition, we use the ANOVA test instead of using the z or t test. Before applying the ANOVA test, we need to check some assumptions for this test. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: All population means for the all variables are same.

Alternative hypothesis: Ha: All population means all variables are not same.

We can also write these hypotheses as below:

Null hypothesis: H0: There is no any significant difference in all population means.

Alternative hypothesis: Ha: There is significant difference exists in the given population means.

After applying this test, we get the test statistic value F for this test and then we can find the p-value for this test. At last, after comparing the p-value with the given level of significance or alpha value, we can take the decision about the null hypothesis regarding the given variables under study.

In the quantitative and qualitative data analysis, sometimes we need to use the tests of independence for the given two categorical variables. In this test we check the claim that whether the given two categorical variables are independent or not. For example, we can check the hypothesis that the gender and education are independent from each other. One of the main important tests in testing the independence between two categorical variables is the chi square test for independence. Let us see this in detail given below:

For checking the independence between the two categorical variables, we use the chi square test for independence. We use this chi square test for independence for the given two categorical variables from the single population. By using this test, we check the claim whether there is any association exists between the given two categorical variables or not. This test consists of some steps. First of all, preparation of the null and alternative hypothesis is very important because we have to decide what we have to prove by using this test. Then after, we fix some level of significance or alpha value for this test. Next step is to find the test statistic value for this test by using the formula given for this test. After finding the test statistic value, we find the p-value for this test. Then after, we can simply compare this p-value with the given level of significance or alpha value, and then we can take the decision regarding the null hypothesis for whether reject the null hypothesis or do not reject the null hypothesis that the given two categorical variables are independent.

## ANOVA Test

Also, there are some other tests for checking independence. We need to use these tests for independence according to available data and assumptions or conditions.

For the section 2, we have to search the five journal articles from the EBSCO or Google scholar. The following articles are taken from the Google scholar. Let us see all these articles step by step given below:

Article 1:

Objectively Measured Sleep Characteristics among Early-Middle-Aged Adults

The CARDIA Study

Abstract

In this article, the researcher finds out the relationship between the number of hours a person sleeping and the risk of cardiac problems. Researcher collects the data of 669 participants in the year 2003 to 2004 and then researcher use this data for statistical analysis. After doing this statistical analysis, researcher draw the conclusions about the relationship between the number of hours person sleeping and the risk of cardiac problems. For this research, researcher used the data of the early middle aged adults.

https://aje.oxfordjournals.org/content/164/1/5.short

Sleep Habits and Patterns of College Students: A Preliminary Study

Abstract:

For this article, researcher studies the sleep habits and patterns of college students. Researcher collects the data for the number of hours student sleep and the marks obtained by the student in the college courses. Then researcher do some statistical analysis and draw some conclusions regarding the numbers of hours student sleeps and the marks obtained by student for different college courses.

https://www.tandfonline.com/doi/abs/10.1080/07448480109596017#.VOHIeO_MT4g

Education and Stratification in Developing Countries

Abstract

This article is based on the study of education and inequality in development in regions. Also this article focuses on the relationship between the educational background and the families financial condition. For this purpose, researcher collects the data for some developing countries and then researcher do some statistical analysis and check his claims. After his research, he found that there is financial gap or economic gap in the different regions due to the education level of families in these regions.

https://www.jstor.org/discover/10.2307/2678615?sid=21105361939691&uid=4&uid=2

Wealth, Expenditures And Decision-Making For Education

Abstract:

This article is based on the wealth, expenditures and decision making for education. Researcher collects the data regarding the wealth; expenditure and education from some region and then researcher do some statistical data analysis. After doing this data analysis, researcher points out the some relationship between these three factors.

https://eric.ed.gov/?id=ED001243

A simulation study of crop growth and development under climate change

Abstract:

In this article, the researcher provides the simulation study of crop growth and development under the different climate change. Researcher collects data from different climatic conditions for the some crop and then researcher finds out that what is the effect of climate changes on the total yield of the crop production and the crop development. For this study, researcher used the different statistical regression models.

https://www.sciencedirect.com/science/article/pii/0168192395022864

In this section, we have to discuss the two articles out of five articles given in the second section. We select the article 1 and 2 for discussion. Let us see the discussions for these articles in detail:

Article 1:

Objectively Measured Sleep Characteristics among Early-Middle-Aged Adults

The CARDIA Study

Abstract

Researcher collects the data for the number of hours the person sleep and the risk of cardiac problem. Researcher collects the data for the year 2003 – 2004. Researcher collects the data for the early middle aged adults. Researcher collects the data for the 669 participants. Researcher collects the data regarding to the time in bed, time required to fall asleep, sleep duration and sleep efficiency. All the participants were of the age group 38 – 50 years. out of the 669 participants, 58% were women. The percentage for the black persons was 44%. For this data, researcher get the mean time in bed was 7.5 hours with the standard deviation 1.2 hours. Researcher found the mean sleep latency time as 21.9 minutes with standard deviation 29 minutes. The mean sleep duration was found as 6.1 hours with the standard deviation 1.2 hours. Mean sleep efficiency was found as 80.9% with standard deviation 11.3%.  Also it was found that average sleep duration for white women as 6.7 hours and for white men, it was observed as 6.1 hours. For black women, it was 5.9 hours and for black men, it was observed as 5.1 hours. Researcher concluded that sleep duration and quality have the consequences for health and it is strongly associated with the race, sex and socioeconomic status of the person.

https://aje.oxfordjournals.org/content/164/1/5.short

Sleep Habits and Patterns of College Students: A Preliminary Study

Abstract:

For this article, researcher collects the data for the college students for the total number of student sleeps and the marks obtained in the college courses. Data is collected for some US college students. Data is collected from the rural and urban areas for checking the relationship between the college performance and the regions. Also, researcher suggest that how the colleges and university officials alter procedures to minimize students’ sleep disturbances and reduce the deleterious effects of sleep problems on  the academic performance.

https://www.tandfonline.com/doi/abs/10.1080/07448480109596017#.VOHIeO_MT4g

References:

1. David Freedman, Robert Pisani, Roger Purves, Statistics, 3rd ed., W. W. Norton & Company, 1997.

2. Morris H. DeGroot, Mark J. Schervish Probability and Statistics, 3rd ed., Addison Wesley, 2001.

3. Leonard J. Savage, The Foundations of Statistics, 2nd ed., Dover Publications, Inc. New York, 1972.

4. Robert V. Hogg, Allen T. Craig, Joseph W. McKean, An Introduction to Mathematical Statistics, 6th ed., Prentice Hall, 2004.

5. George Casella, Roger L. Berger, Statistical Inference, 2nd ed., Duxbury Press, 2001.

6. David R. Cox, D. V. Hinkley, Theoretical Statistics, Chapman & Hall/CRC, 1979.

7. Peter J. Bickel, Kjell A. Doksum, Mathematical Statistics, Volume 1, Basic Ideas and Selected Topics, 2rd ed. Prentice Hall, 2001.

8. T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach, Academic Press, Inc., New York, 1967

9. Harald Cramér, Mathematical Methods of Statistics, Princeton, 1946

10.Laubach RS, Koschnick K. Using Readability: Formulas for Easy Adult Materials. Syracuse, NY: New Readers Press, 1977.

11. SPSS-X Users Guide. 3rd edition. Chicago. IL: SPSS, Inc., 1988.

12.Doak L, Doak C. Patient comprehension profiles: recent findings and strategies. Patient Couns Health Educ. 1980;2:101–6. “

13.Anthony, R. N. and Herzlinger, R. E. (1980). Management Control in Nonprofit Organizations. Homewood, Ill: Irwin.

14. Balderston, F. E. (1975). Managing Today's University. San Francisco: Jossey-Bass.
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