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Review andresponse to D3.4, D3.5, and D3.6. Summarize their findings and indicate areas of agreement, disagreement, and improvement. Support your views with citations and include a reference section. Provide a title block that includes who you are reviewing.

The process of data transformation is an aspect of data analysis that is sometimes called file management and can be quite a mundane process for the researcher. Even though this process is tedious, it is essential for the researcher to accomplish because introducing errors into the data can corrupt the overall study.

There are four data transformations that are useful to the researcher. The data transformations are count, recode, and two ways to compute a new variable that is the sum or average of several variables. The data used for this study was hsbdata (Morgan, Leech, Gloeckner, & Barrett, 2013). The next section will discover recoding variables.

**D3.1a**

In this section, the researcher will relay why it is best to recode father’s education and mother’s education. There are times when it is easier to work with a smaller number of categories versus many categories. Recodes are used to combine two or more small groups or categories of a variable so that group size will be large enough to perform statistical analyses. The text gives an example of having a small number of fathers or mothers who have a master’s or doctorate so it would make sense to combine them with bachelor’s degrees and call the category “B.S. or more” (Morgan et al., 2013).

**D3.1b**

In this section, the researcher will relay when the researcher should not recode normal/scale level variables into two or three categories. The variables of father’s education and mother’s education are considered ordinal variables. It is not recommended to divide into two categories or divide into three categories an ordinal or a normal/scale variable in which all of the levels are ordered correctly and are meaningfully different from one another (Morgan et al., 2013).

**D3.2 Computing Variables**

In working with the variables of parent’s education, there are some very compelling reasons to compute the parent’s education. In combining the father’s education and the mother’s education scores, the researcher will discover that the data are highly correlated. It is better to treat this data as one variable. In doing this, the researcher can demonstrate the use of the Mean function within the SBSS program. The Mean function is a type of Compute function within the SBSS program.

In this case, it seems only reasonable for the researcher to use only the mother’s education is the father’s education is unknown. It would be even more beneficial to compute parents’ education if there were many students whose father’s education was unknown, which many times is the case. History has proven that most students know their mother’s education. By utilizing the Mean function in the SBSS program, almost all the students would have a parents’ education score (Morgan et al., 2013).

**D3.3 Evaluating Data**

In evaluating the data of Output 5.5, Descriptive Statistics, the researcher will note some fascinating data. This table was created so that the researcher can check for errors and the normality of the new variables. Output 5.5 shows the researcher the descriptive statistics of five variables. Those five variables are math courses taken, father’s educ revised, mother’s educ revised, pleasure scale, and parents’ education (Morgan et al., 2013).

In the Output 5.5, descriptives statistics the pleasures scale reveals a skewness of -.682. Although it is a negative number, the skewness does fall within the parameters of the normal distribution of being less than 1. If the absolute values of the skewness statistic are less than 1 for pleasure scale, consider the variable to be approximately normally distributed. For the variable of math courses taken the skewness statistic is .325. This skewness also falls within being less than 1. Because it is less than 1, then it is also considered to be approximately normally distributed (Morgan et al., 2013).

**D3.4 Interpreting Statistics**

The researcher must take into consideration the statistical significance of the data. The calculated value is compared to a critical value that takes into account the degrees of freedom. These degrees of freedom are usually based on the number of participants within the study. The SBSS program provides a probability value. This probability value is called sig. for significance. The significance level refers to the probability of a Type I error, which in turn is the probability of rejecting the null hypothesis when it is true. The sig. or *p* value is calculated by the SBSS program. If the probability is less than the preset alpha level, which is usually .05, the researcher can say that the results are statistically significant or that they are significant at the .05 level. The researcher can also say that the null hypothesis of no difference or no relationship can be rejected (Morgan et al., 2013).

**D3.5 Choosing Statistics I**

Choosing the appropriate statistics can be a very daunting process for a researcher. The researcher has numerous tools that will help in choosing the appropriate statistic for variables, levels, and design. The text introduces an eight-step decision tree to help the researcher select the appropriate inferential statistic. The first question the researcher will ask is how many variables are there in the research question or hypothesis? This decision tree refers to Tables 6.1 – Table 6.4 in chapter 6 of the text. If there are two variables, use the basic statistic. Step two explains that the researcher should use Table 6.1 if the independent variable is nominal or has 2-4 levels. At this point, the researcher should determine the number of levels of the independent variable. Discover what the design is, whether it is within, repeated, or related. A measurement of the dependent variable will also need to be discovered. Step three explains that if both variables are nominal, then the researcher will need to use the bottom row of Table 6.1 or 6.2. Step four explains that if both variables have five or more ordered levels, then the researcher should use the top rows of Table 6.2 (Morgan et al., 2013).

If there are three or more variables, use the complex statistic. If the dependent variable is normal/scale, then the researcher would go to step five and six. Step five explains that if the independent variables are nominal or have a few ordered levels to use the top row of Table 6.3. Step six relays that if the independent variables are normal/scale or dichotomous use the top row of Table 6.4. If the dependent variable is not normal/scale and is nominal or dichotomous, then the researcher should use the bottom row of Table 6.3 or 6.4. If there are two or more moderately related dependent variables considered together, then the researcher would use step eight. Step eight relays that the researcher should use the general linear model to do MANOVA (Morgan et al., 2013).

**D3.6 Choosing Statistics II**

If the researcher wanted to see if there were a difference between three ethnic groups in math achievement the researcher would use a basic statistic. There are certain things that the researcher must look for to know which category in Table 6.1 will work for the data. The following questions will need to be answered. The researcher will need to know if there are three levels of the independent variable, in this case, there are. The researcher will need to know how many dependent variables are there? In this case, there is one dependent variable, and that variable is math achievement. The researcher will need to check whether the variable is normal or scale? In this case, the variable is normally distributed. By utilizing Table 6.1 in the text, the researcher can know that the one-way analysis of variance (ANOVA) can be used between groups study (Morgan et al., 2013).

**D3.7 Choosing Statistics III**

When determining what statistic would be used if one independent variable, geographic location, and one dependent variable, satisfaction with living environment, the researcher would begin by determining how many variables there are in the research question or hypothesis. If there are two variables, then the researcher would use the basic statistic.

The measurement of the dependent variable, satisfaction with environment, is nominal/dichotomous. The dependent variable is measured at dichotomous levels, yes and no, by using Table 6.1 in the text, the rule of Chi-square test statistic would apply in this case (Morgan et al., 2013).

References

Morgan, G. A., Leech, N. L., Gloechner, G. W., & Barrett, K. C. (2013). *IBM SBSS introductory statistics: Use and interpretation*

(5th ed.). New York: Brunner-Routledge.