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Review a students response to D3.4 , D3.5 D3.6 Summarize their findings and indicate areas of agreement, disagreement and improvement. Support your views with citations and include a reference section.
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D3.1, Recoding Variables
According to Morgan et al. (2013), there are two reasons why a researcher might want to recode variables. First, it might be necessary to recode if the category values might provide an inconsistent sequence. The text gives an example of the parent’s education. A value of 5 represents 2 years at a vocational school while a value of 6 indicates less than 2 years at a four-year college or university. Morgan et al. (2013) point out that a student with an earned associates degree from a vocational school would correctly select a score of 5 on this variable while a student who completed a year at a four-year school would also correctly score a 6. The 6 score would indicate more education for the second student, which of course is not the case. Recoding, as we did in the exercise, can remove this inconsistency with new categories that do not specify the type of school, but only the duration of education completed.
Another reason mentioned in the text for recoding of variables is to reduce the number of categories that do not have a sufficient number of responses for statistical analysis (Morgan et al., 2013). For example, in our data set, only one student reported more than 2 years of college but not completing a degree. This lack of response can make analysis on this category difficult or impossible. So, it may be more meaningful to reduce the number of categories, say, to include a category called “Some College,” which will allow more cumulative responses.
D3.2, Computing Variables
I see two reasons why we would want to compute a parents’ education score as opposed to simply using the individual parent (mother and father) scores. First, because, as it turns out, the scores of the individual parent’s education scores are correlated (Morgan et al., 2013). For future analysis, it makes sense to combine them into a single variable. Second, the combined parents’ scores reduce skewness and approximate a normal distribution. The skewness mearues of the individual scores (mother and father) were much more pronounced and in fact the mother’s education responses fell outside the range that approximated normal. By combining the parent’s education into a single variable, the applicability of normal distributions is attained.
D3.3, Evaluating Data
The skewness score for the “pleasure scale” variable is -.682 as shown in the Descriptives table in Output 5.5 (Morgan et al., 2013, p. 85). The absolute value of that score is between 0 and 1, so the conclusion should be that this variable is normally distributed. The “math courses taken” variable has a skewness statistic of .325 which means that the distribution of scores approximates normal.
D3.4, Interpreting Statistics
For a p value of less than .05, it means that the probability of rejecting the null hypothesis when it is actually true is less than 5% (Morgan et al., 2013). The null hypothesis is the statement that there is no correlation between the independent and dependent variables. When the p value is less than .05, it indicates statistical significance, that there is relationship between the variables and that the null hypothesis can be rejected.
D3.5, Choosing Statistics I
Information about the variables, levels and design are important to identify in order to work through the decision tree presented in Figure 6.1 in the text (Morgan et al., 2013, p. 93). The first question asks how many variables are being considered. The answer should include both independent and dependent variables. The answer provided will direct the reader to one of four tables, also in the text, according to the branch in the tree. Before leaving the tree to examine the tables, if the answer is three or more to the number of variables, then another two questions asking the number of dependent variables and the type of variables need to be addressed.
Now confronting the four tables (Tables 6-1, 6-2, 6-3 and 6-4) as found on pages 95-97 of the text, certain inputs are required to utilize the tables correctly (Morgan et al., 2013). One input is the number of levels in the independent variable. Two categories position the reader into one set of columns while three or more categories direct to a different set of columns. Another input is the variable type, which will generally drive the reader to a specific row of the tables. A normal variable will be treated differently (i.e. be in a different row of the table) than an ordinal or nominal / dichotomous variable, which would identify different rows. Finally, the research question designs further segment the approach in the tables. A design that is between-groups will likely be directed differently from a design employing within-subjects. Identifying this information on variables, levels, and design before starting through the path of the decision tree and the resulting tables will make the process more obvious and sequential.
D3.6, Choosing Statistics II
Let’s start with noting the informational details from the previous answer about the current question. We have two variables: the ethnicity is the independent variable and math achievement score is the dependent variable. Using the decision tree in Figure 6.1 of the text (Morgan et al., 2013 p. 93), an answer of two directs us to one of three options depending on the types of our two variables. Ethnicity is a nominal variable (no ordering) while math achievement approximates a normal distribution. Based on these two answers, we are positioned in box (2) in the tree and thus directed to Table 6.1 on page 94. Because our dependent variable (math achievement score) approximates normal, we should use the first row of the table. The ethnicity independent variable has three or more levels, so we are directed to the right-most set of columns in the table. Finally, we consider the design which is between-groups. This answer positions us in the second column from the right in the table. The box that is the intersection of the normal data (row 1) and the three or more between-groups data (column 3) yields an inferential statistic of one-way ANOVA.
D3.7, Choosing Statistics III
Starting again with the informational details, the following is noted. There are two variables: geographic location is the independent variable and satisfaction with living environment is the dependent variable. The location has four levels (north, south, east and west) without ordering and is thus a nominal variable. The dependent variable has two levels (yes or no) and is thus a dichotomous, unordered variable. The design is again between-groups. Using the decision tree in Figure 6.1 of the text (Morgan et al., 2013 p. 93), an answer of two nominal variables directs us to box 3. The research question is one of difference between groups. As a result, Table 6.1 should be selected for difference questions. So, three or more levels in the independent variable combined with a nominal dependent variable with a between-groups design direct us to the second box from the right on the last row of the table. There the preferred inferential statistic is the chi-square.
Reference
Morgan, G., Leech, N., Gloeckner, G., & Barrett, K. (2013). IBM SPSS for introductory statistics (5th ed.). Taylor & Francis.

Explanation & Answer

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Running head: STATISTICS RESPONSES
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Statistics Responses
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STATISTICS RESPONSES
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D3.4, Interpreting Statistics
In this discussion, you found that the value of P that is less than 0.05 indicates that the
probability of not accepting the null hypothesis is less than 5%. Based on your findings, I agree
with you that a p whose value is less than 0.05 symbolizes that there is statistical significance and
that the hypothesis should not be applied. Statistical significance shows that there exists a
correlation between variables. Since the null hypothesis means tha...
