# Discussion Replies 3

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**Please respond to the 4 discussion responses below. The reply must summarize the student’s findings and indicate areas of agreement, disagreement, and improvement. It must be supported with scholarly citations in the latest APA format and corresponding list of references to each response. The minimum word count for Integrating Faith and Learning discussion reply is 250 words.**

**1. Kandice**

**D3.4.1 Using Outputs 4.1a and 4.1b: (a) What is the mean visualization test score? (b) What is the skewness statistic for math achievement test? What does this tell us? (c) What is the minimum score for the mosaic pattern test? How can that be?**

D3.4.1 (A) The mean visualization test score is 5.2433

D3.4.1 (B) The skewness statistic for math achievement test is .044 and this tells us that a skewness value that is greater than 1 or less than -1 indicates a highly skewed distribution. If the value is between 0.5 and 1 or -0.5 and -1 is moderately skewed. However, if a value is between -0.5 and 0.5 that tells you that the distribution is symmetrical.

D3.4.1(C) The minimum score for mosaic pattern test has a minimum test score of -4.0 and this can be due to one single student receiving the lowest possible score within the range of test scores that are reported.

**D3.4.2.Using Output 4.1b: (a) For which variables that we called scale, is the skewness statistic more than 1.00 or less than –1.00? (b) Why is the answer important? (c) Does this agree with the boxplot for Output 4.2? Explain.**

D3.4.2(A) The variables that we called scale, when the skewness statistic more than 1.00 or less than –1.00 would be the competence scale.

D3.4.2(B) The answer is important because it lets the end user understand the importance of the information that was presented.

D3.4.2 ( C ) The non-normal indication noted in D3.4.2.a and D3.4.2.b for the competence scale variable agrees with the boxplot containing this variable in Output 4.2b (Morgan et al., 2020). In this output, it is obvious that the whiskers are nowhere near even in length and the box line is also quite far from the middle point. There are also three additional low-scoring outliers which fall below the already exaggerated “low” whisker. It is clear through both methods of assessment that the competence scale variable is very skewed.** **

**D3.4.3.Using Output 4.2b: (a) How many participants have missing data? (b) What percent of students have a valid (non-missing) motivation scale or competence scale score? (c) Can you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale and competence scale scores? Explain.**

D3.4.3 (A) Based on the data presented within the output from 4.2b there are four participants that have missing data.

D3.4.3 (B) The percentage of students that have a valid (non-missing) motivation scale or competence scale score is 94.7% so this means that the majority of the participants provided the needed information. Understanding the sample information will allow the end user to have a clear understanding of what is being presented (Priam, 2020).

D3.4.3 (C ) From outputs 4.1there is one participant that is missing the motivation scale and competence scale scores, and 4.2b there are four participants that are missing both the motivation scale and the competence scale scores.

**D3.4.4.Using Output 4.4: (a) Can you interpret the means? Explain. (b) How many participants are there altogether? (c) How many have complete data (nothing missing)? (d) What percent are in the fast track? (e) What percent took algebra 1 in h.s.?**

D3.4.4 (A) This means within the data that is provided within the output is the average values for the data points that are being considered and discussed within the diagram.

D3.4.4 (B) There are 75 participants there altogether.

D3.4.4 ( C) There are 75 participants that have complete data with nothing missing.

D3.4.4 ( D) The percent that are on the fast track is 45.3%.

D3.4.4 (E) The percentage of participants that took algebra 1 in high school is 59

**D3.4.5.Using Output 4.5: (a) 9.6% of what group are Asian-Americans? (b) What percent of students have visualization 2 scores of 6? (c) What percent had such scores of 6 or less?**

D3.4.5 ( A) 9.6% of the valid percent group are Asian-Americans meaning these individuals have provided valid information for each data set within the frequency table.

D3.4.5 (B ) Based on the data provided the number of students that have a visualization 2 scores of 6 is 5.3%.

D3.4.5 ( C) Output 4.5 also shows that 66.7% of the 75 surveyed students had visualization 2 scores of 6.00 or lower (Morgan et al., 2020). This can be found by referring to the “cumulative percent” column in the frequency table. It is possible to glean this information since the table lists the visualization 2 values from lowest to highest.

**References**

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics: Use and Interpretation: Use and Interpretation. Routledge.

** **Priam ,R. (2020). Visualization of generalized mean estimators using auxiliary information in survey sampling, *Journal of Communications in statistics, Theory Methods,49*(18),4468-4489.

2. Yanitza

**D3.4.1 Using Outputs 4.1a and 4.1b:**

- What is the mean visualization test score?
- The mean in the visualization score is 5.2433.

- What is the skewness statistic for math achievement test? What does this tell us?
- The skewness statistic for math achievement is .044 with a standard error of .277. The skewness determines how much the variable deviates from the normal distribution. In this case the skewness was divided by the standard error for a result of 1.58. This means the result is away from the normal curve by .58 with a tail leaning to the right with no significant difference.

- What is the minimum score for the mosaic pattern test? How can that be?
- The minimum score for mosaic pattern test is -4.0. The mosaic pattern has a variance of 91.658 meaning that by having a -4.0 in the minimum and a maximum of 56.00 with a range of 60 it has been an error in the measure. The variance is distant from the range.

**D3.4.2. Using Output 4.1b:**

- For which variables that we called scale, is the skewness statistic more than 1.00 or less than –1.00?
- The variables normal and ordinal are called scales. If the value of the skewness is less than one, then the variable is normal. If the ordinal variable has a skewness between -1 and 1 are in the assumption of normality or normal distributed variables.

- Why is the answer important?
- The skewness of a probability distribution is crucial for many measures. Over the years different measures have been proposed to compare distributions with their skewness (Eberl & Klar, 2020). It is essential to check the skewness and variables to make sure there are no errors in the measure.

- Does this agree with the boxplot for Output 4.2? Explain.
- The scale will agree with the boxplot because it will measure multiple combinations of variables. If boxplot is used it can be a better understanding of the data.

**D3.4.3. Using Output 4.2b:**

- How many participants have missing data?
- Table 4.2b shows that in the 71 valid cases, 4 of them are missing data.

- What percent of students have a valid (non-missing) motivation scale or competence scale score?
- The percentage is 94.7% of valid non missing motivation scale or competence scale score.

- Can you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale and competence scale scores? Explain.
- By analyzing the output 4.2b there is 5.3% that is missing. In output 4.1 please notice that there is two participants missing for the competence scale and the motivation scale each.

**D3.4.4. Using Output 4.4:**

- Can you interpret the means? Explain.
- The mean is the average between the variables and the score used. There are no missing data in output 4.4 and the mean represents no meaning for nominal variables with more than two categories.

- How many participants are there altogether?
- There are a total of 75 participants for each of the variables.

- How many have complete data (nothing missing)?
- There is no missing data in output 4.4.

- What percent are in the fast track?
- The results show that 55% are on the regular track meaning that 45% was on the fast track.

- What percent took algebra 1 in h.s.?
- The results show that .79% took algebra 1 h.s.

**D3.4.5. Using Output 4.5:**

- 6% of what group are Asian-Americans?
- The output that represents the ethnicity group will be the one with the variable representing the Asian-American.

- What percent of students have visualization 2 scores of 6?
- The percentage of students with a score of 6 in visualization 2 is 70.55%. This represent and average of the two scores of 6 with a percentage of 74.7 % and 66.7

- What percent had such scores of 6 or less?
- There is four variables that represent a score of 6 or less with a percentage of 80%, 78.7%,74.7% and 66.7% for a total average of 75.02%.

Reference

Eberl, A., & Klar, B. (2020). Asymptotic distributions and performance of empirical skewness measures. *Computational Statistics & Data Analysis*, *146*, 106939. https://doi.org/10.1016/j.csda.2020.10693Links to an external site.

Morgan, G. A. (2020). *IBM SPSS for introductory statistics: Use and interpretation*. Routledge.

**3. kenneth**

**Chapter 4, Question 1.a.**

**Chapter 4, Question 1.a.**

The mean visualization test score is 5.2433.

**Chapter 4, Question 1.b.**

**Chapter 4, Question 1.b.**

The skewness score for the math achievement test is .044. This tells us that the data is very close to symmetric as any skewness score +/- .5 indicates the distribution is approximately normal.

**Chapter 4, Question 1.c.**

**Chapter 4, Question 1.c.**

The minimum score for the mosaic pattern test is -4.0. While it is not clear from the data set if a negative score could be achieved, this researcher is assuming that any test has an absolute zero, making this scale variable a ratio scale. As such, negative numbers in the data set would indicate an error. This conclusion is further supported by the fact that there is only one entry in which the data is negative, and it is more than three standard deviations from the mean.

**Chapter 4 Question 2 – Outputs 4.1b**

**Chapter 4 Question 2.a.**

**Chapter 4 Question 2.a.**

The scale variable for which the skewness statistic more than 1.00 or less than –1.00 is the competence scale, for which the skewness statistic is -1.634.

**Chapter 4, Question 2.b.**

**Chapter 4, Question 2.b.**

This is important because it indicates that the data is not normally distributed and that the researcher’s labeling of this variable as scale is likely incorrect. Instead, this variable should likely be labeled as ordinal.

**Chapter 4, Question 2.c.**

**Chapter 4, Question 2.c.**

The boxplot in Output 4.2 for the competence variable is consistent with the skewness statistic discussed above. This author knows this because the box plot demonstrated a median closer to the 75% quartile and the upper quartile whisker is condensed compared to the lower quartile. Furthermore, the boxplot indicates 4 outlying data points that should be examined to determine validity.

**Chapter 4, Question 3 – Output 4.2b**

**Chapter 4, Question 3.a.**

**Chapter 4, Question 3.a.**

5.3% (4/75) of participants have missing data.

**Chapter 4, Question 3.b.**

**Chapter 4, Question 3.b.**

The percentage of students with valid (non-missing) motivation scale or competence scale score is 97.33% for both variables and population sets (73/75).

**Chapter 4, Question 3.c.**

**Chapter 4, Question 3.c.**

You can tell from Output 4.1b the number of students with valid motivation and competence scale scores. Output 4.2b indicates 71 students have valid motivation and competence scale scores. As Morgan et al. (2020) note, the underlying syntax utilized to develop this analysis indicates that if either group was missing data for the specific variable, then information for that specific student case (student) would be omitted from both box plots. Knowing this, the researcher can surmise that the valid case data provided in Output 4.1b is indicative of 4 separate students not having valid case data.

**Chapter 4, Question 4 – Output 4.4**

**Chapter 4, Question 4.a.**

**Chapter 4, Question 4.a.**

The means cannot be interpreted because dichotomous variables are nominal by nature. However, given that dichotomous variables only have two potential outcomes, the determining of the mean for dummy coded variables (i.e. 0,1) can indicate group size relative to the other (Morgan et al., 2020). In the case of dummy coding as described above, the percentage of the group coded as one can be determined by multiplying the mean by 100.

**Chapter 4, Question 4.b.**

**Chapter 4, Question 4.b.**

There are 75 participants for each variable.

**Chapter 4, Question 4.c.**

**Chapter 4, Question 4.c.**

The “valid N (listwise) indicates that all 75 participants have valid data.

**Chapter 4, Question 4.d.**

**Chapter 4, Question 4.d.**

For the academic track variable, regular was coded as 1 and fast track as 0. Given that the mean for this variable in Output 4.4 is 55%, this would indicate that the percentage of students in the fast track can be determined by subtracting the mean from the entire population, represented by 1 (or 100%). Therefore, 1-.55=.45, or 45% of the population, is in the fast track.

**Chapter 4, Question 4.e.**

**Chapter 4, Question 4.e.**

Given students who have taken algebra 1 in high school were coded as 1, and those who did not as 0, then the percentage of students who have taken algebra in high school can be determined by multiplying the mean in Output 4.4. by 100; resulting in 79%.

**Chapter 4, Question 5 – Output 4.5**

**Chapter 4, Question 5.a.**

**Chapter 4, Question 5.a.**

9.6% of students submitting valid data are Asian-Americans.

**Chapter 4, Question 5.b.**

**Chapter 4, Question 5.b.**

8% of students have visualization 2 scores of 6.

**Chapter 4, Question 5.c.**

**Chapter 4, Question 5.c.**

56% (42/75) had visualization 2 scores of 6 or less.

**References**

Morgan, G., Barrett, K., Leech, N., and Gloeckner, G. (2020). *IBM SPSS for introductory **statistics: Use and interpretation*. (6th ed.). Routledge.

4. Robert

**D3.4.1 Using Outputs 4.1a and 4.1b: (a) What is the mean visualization test score?**

According to Morgan et al. (2020) the mean visualization score is listed in Output 2.1b. This score is listed as 5.2433.

**(b) What is the skewness statistic for math achievement test? What does this tell us?**

The skewness statistic for the math achievement test is .04. Morgan et al. (2020) states that the closer to zero the more normally distributed the dataset is. In the math achievement test the skewed meets the -1 to 1 for the skewness statistic to show normal distribution.

**(c) What is the minimum score for the mosaic pattern test? How can that be?**

The Minimum statistic is -4.0 on a mosaic pattern test. This could have been an error as logic might state a participant cannot score negatively on a test. However, after checking the Code book the scale for the Mosaic test ranges from -4 to 56. This just means that at least one participant scored the lowest possible score.

**D3.4.2.Using Output 4.1b: (a) For which variables that we called scale, is the skewness statistic more than 1.00 or less than –1.00? (b) Why is the answer important?**

Morgan et al. (2020) states that the closer to zero the more normally distributed the dataset is. In the math achievement test, the skewed meets the -1 to 1 for the skewness statistic to show normal distribution.

** (c) Does this agree with the boxplot for Output 4.2? Explain.**

The statistic for the competency scale does agree with the box plot in 4.2. This scale has multiple extreme measures that lay outside of the upper level. This means that there is a significant negative skew to the data. This aligns with the box plot showing that most of the answers are in the lower end of the spectrum.

**D3.4.3.Using Output 4.2b: (a) How many participants have missing data? (b) What percent of students have a valid (non-missing) motivation scale or competence scale score? (c) Can you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale and competence scale scores? Explain.**

In 4.2b 71 students are listed as having scores for the motivational scale and competence scale. 4 were missing from one or the other according to the case processing so they would have been omitted from both scales since the analysis involves list-wise deletion (Morgan, Barrett, Leech, & Gloeckner, 2020). This means that 94.67 percent of the students had valid motivational and competence scores. While the N of each category is listed, there is no manner to determine from 4.2b if the same participant was missing input for both variables or just one of the other.

**D3.4.4.Using Output 4.4: (a) Can you interpret the means? Explain. (b) How many participants are there altogether? (c) How many have complete data (nothing missing)? (d) What percent are on the fast track? (e) What percent took Algebra 1 in h.s.?**

The means for 4.4 are the most useful column. According to Morgan et al. (2020), a dichotomous variable is a variable with two levels usually coded for one or two. In the academic track, it means 55% of the 75 students are in the regular track. For Algebra 1 the levels are yes/no or true false to show that the participant has taken algebra1. Listing the means will also provide an error checking as it is highly unlikely the mean for calculus will be larger than Algebra 1. There are 75 participants and all have valid data. This is shown as the Valid N and the valid N is list-wise. There are approximately 33 students who are on the fast track and approximately 59 participants have taken Algebra 1.

**D3.4.5.Using Output 4.5: (a) 9.6% of what group are Asian-Americans? (b) What percent of students have visualization 2 scores of 6? (c) What percent had such scores of 6 or less?**

Asian Americans make up 9.65 of the valid N, meaning non-missing data, or 9.6% of the 73 students who answered that question. 8% of Visualization scores have a 6 for their score. 66.7 % had a score of 6 or less this is located in the cumulative percent column.

# References

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). *IBM SPSS for Introductory Statistics Use and Interpretation.* New York, NY: Routledge.

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