Please respond to the 3 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. Julius

**D2.3.1. Measurement Type**

**If you have definite, ordered data (such as low income, middle income, high income) what type of measurement would you have? Why?**

According to Morgan et al. (2019), if one’s data were categorized and arranged, one would have ordinal measurements. According to the authors, ordinal measurement is suggested for this type of data due to its ability to depict the ordered character of the categories without requiring equal intervals or normal distribution.

**D2.3.2. (a) Compare and contrast nominal, dichotomous, ordinal, and normal variables.**

According to Morgan et al. (2019), categories without any sorting, like gender or race, are represented by nominal variables. Only yes/no or true/false values can be assigned to a dichotomous variable (Morgan et al., 2019). Ordinal variables classify individuals based on objective criteria, such as their degree of education or social standing (Morgan et al., 2019). We might think of weight and temperature as normal variables (interval or ratio) with an absolute zero point and a continuous range of values in between

(Morgan et al., 2020).

**(b) In social science research, why isn’t it important to distinguish between interval and ratio variables?**

Due to their similarity in nature and statistical features, researchers in the social sciences generally find it unnecessary to differentiate between interval and ratio variables (Morgan et al., 2019). According to the authors, there is a technical distinction between ratio data and interval data that the ratio data has an absolute zero point, and interval data does not. However, Morgan et al. (2019) claim that it is irrelevant to most scholars to conduct studies while treating interval and ratio data identically without significantly impacting results or conclusions.

**D2.3.3. What percent of the area under the standard normal curve is within one standard deviation of (above or below) the mean? What does this tell you about scores that are more than one standard deviation away from the mean?**

The normal distribution has 68% of its area above the mean, 34% of its area below the mean, and 34% of its area right in the middle. However, within one standard deviation, the actual proportion is 34.13 percent. This translates to around 32% of all scores being more than one standard deviation outside the mean.

**D2.3.4. (a) How do z scores relate to the normal curve? (b) How would you interpret a z score of –3.0? (c) What percentage of scores is between a z of –2 and a z of +2? Why is this important?**

**(a) How do z scores relate to the normal curve?** – According to Johnson (2013), Z scores reflect the number of standard deviations above or below the mean of a normal distribution. Hence they connect to the normal curve.

**(b) How would you interpret a z score of –3.0? – **If the z-score is -3.0, the value is three standard deviations below the mean.

**(c) What percentage of scores is between a z of –2 and a z of +2? Why is this important? **The fact that 95 percent of results fall within the z-score range of -2 to +2 is crucial because it allows us to calculate the fraction of results within a specific range and to make direct comparisons between results from different distributions.

**D2.3.5. Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data?**

According to (Morgan et al., 2019), displaying nominal data with frequency polygons is inappropriate since these shapes have no intrinsic hierarchy. Instead of using a table, a bar chart is more appropriate for showing the nominal data since the height of each bar can be easily adjusted to show the relative proportion of each category (Morgan et al., 2019).

**Conclusion**

Choosing the appropriate data format for the outcome measures is an essential first step in analyzing the findings of practical studies. The data quality determines the extent to which an intervention may be evaluated. Definitions, attributes, and interpretations of standard measures of intervention impact are outlined, and suggestions are offered for estimating the effectiveness of interventions based on the kinds of information often presented in places like academic journals. A companion document provides statistical procedures to estimate the effects of the most used effect measures (Higgins et al., 2019). The z-score is the standard deviation-based distance from a data point to the mean. Both positive and negative values can be assigned to a score. The sign indicates whether an observation is more than or below the mean.

**References**

Higgins, J. P., Li, T., & Deeks, J. J. (2019). Choosing effect measures and computing estimates of effect. Cochrane handbook for systematic reviews of interventions, 143-176. https://doi.org/10.1002/9781119536604.ch6

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2019). IBM SPSS for Introductory Statistics Use and Interpretation (6th ed.). New York, NY, USA: Routledge.

2. Rita

**D2.3.1 If you have categorical, ordered data (such as low income, middle income, high income) what type of measurement would you have? Why?**

D2.3.1 When having categorical, ordered data (such as low-income, middle-income, and high-income), the measurement would be ordinal. In the ordinal scale, the higher number is determined by the categories that are rated higher or have more or something, but the categories are not equal (Morgan et al., 2020).

**D2.3.2 (a) Compare and contrast nominal, dichotomous, ordinal, and normal variables. (b) In social science research, why isn’t it important to distinguish between interval and ratio variables?**

D2.3.2 (a) The nominal variable is the most basic level of measurement that assigns a name to three or more uncategorized categories; dichotomous variables always have only two categories, and, in some cases, they have implied order; ordinal variables have three or more ordered categories from low to high with frequency distribution and scores are not normally distributed, and normal variables can have as many as at least five ordered levels with frequency distributed being approximately normal (Morgan et al., 2020). (b) In social science, it is not essential to distinguish between interval and ratio variables because, according to Morgan et al. (2020), all types of statistics that are available can be done with interval data, and both categorized as quantitative variables.

**D2.3.3. What percent of the area under the standard normal curve is within one standard deviation of (above or below) the mean? What does this tell you about scores that are more than one standard deviation away from the mean?**

D2.3.3 34% of the area is under the standards of the normal curve within one deviation above or below the mean (Morgan et al., 2020). Since 68% of the average area curve is within one standard deviation from the mean, then 32% lies away from the mean (Morgan et al., 2020).

**D2.3.4 (a) How do z scores relate to the normal curve? (b) How would you interpret a z score of -3.0? (c) What percentage of scores is between a z of -2 and a z of +2? Why is this important?**

D2.3.4 (a) Z scores relate to the normal curve by converting the normal curves into standard normal curves and setting the mean equal to zero since all normal curves have the same proportion of the curve within a standard deviation, for example, one standard deviation, two standard deviations and so on (Morgan et al., 2020). (b) A score of a z -3.0 is described as the standard deviation being less than the mean. (c) 95 is the percentage of scores between a z -2 and a z +2. (Morgan et al., 2020). The z score is essential because it helps identify how far the item drifts away from the distribution mean (Morgan et al., 2020).

**D2.3.5 Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data?**

D2.3.5 According to Morgan et al. (2020), frequency polygons are best used with approximately normal data. Frequency polygons can also be used with ordinal data—bar charts best display nominal data (Morgan et al., 2020).

**References:**

Morgan, G.A., Barrett, K.C., Leech, N.L., & Gloeckner, G.W. (2020). *IBM SPSS for Introductory Statistics: Use and Interpretation* (6th ed). Routledge.

3. Karli

**D2.3.1 – If you have categorical, ordered data (such as low-income, middle-income, high-income) what type of measurement would you have? Why?**

If you have categorical, ordered data, the type of measurement you would have needed to utilize is ordinal. Ordinal measurements are not only mutually exclusive categories but instead are ordered from low to high where ranks could be assigned (Morgan, Leech, Gloeckner, Barrett, 2020). Ordinal data could include measurements broken down into categories such as low-income, middle-income, and high-income.

**D2.3.2 – Variable Comparison**

**(a) Compare and contrast nominal, dichotomous, ordinal, and normal variables.**

**(a) Compare and contrast nominal, dichotomous, ordinal, and normal variables.**

When comparing and contrasting nominal, dichotomous, ordinal, and normal variables, there are several points of similarity as well as several distinguishing factors. Nominal variables are represented by numerals assigned to each category that stand for the name of the category but have no implied order or value whereas ordinal variables are not mutually exclusive categories, but the categories are ordered from low to high (Morgan, Leech, Gloeckner, Barrett, 2020). Dichotomous variables always have two levels and, in some cases, have an implied order, and normal variables are represented by normally distributed data with ordered levels from minimum to maximum (Morgan, Leech, Gloeckner, Barrett, 2020). The key difference between these types of variables can be determined by whether or not order is a necessary factor and the type of categories being taken into consideration. Each variable type has a distinguishing factor that aids in determining its appropriate usage.

**(b) In social science research, why isn’t it important to distinguish between interval and ratio variables?**

In social science research, it is not vital to distinguish between interval and ratio variables. Interval variables are ordered levels in which the difference between levels is equal but there is no true zero whereas ratio variables are ordered levels in which the difference between levels is equal but there is a true zero (Morgan, Leech, Gloeckner, Barrett, 2020). Although these variable types are important in some types of research, for social sciences attribute independent variables are especially important in place or interval and ratio variables as they are both quantitative variables and claims cannot be made about ordinal data.

**D2.3.3 – What percent of the area under the standard normal curve is within one standard deviation of (above or below) the mean? What does this tell you about scores that are more than one standard deviation away from the mean?**

Approximately 34% of the area under the standard normal curve is within one standard deviation of above or below the mean therefore when taking one standard deviation both above and below the mean 68% of the areas under the standard normal curve would be taken into consideration (Morgan, Leech, Gloeckner, Barrett, 2020). Understanding that 68% of the area under the standard normal curve falls within one standard deviation provides a clear indication that scores that are more than one standard deviation away from the mean are rarer. Although it is not extremely uncommon to have scores fall within two standard deviations, the further away the score is from the mean the rarer the occurrence.

**D2.3.4 – Z Score Interpretation**

**(a) How do z scores relate to the normal curve?**

Z scores are important variables when reviewing the normal curve. When examining the normal curve table, the areas under the curve for one standard deviation are represented by z = 1, two standard deviations as z = 2, and so on and so forth (Morgan, Leech, Gloeckner, Barrett, 2020). The z score is also referred to as the standard score as it allows the probability of a score to be calculated and compared within a normal distribution (Morgan, Leech, Gloeckner, Barrett, 2020). The z-score on a normal curve could be analyzed when normally distributed data is being reviewed.

**(b) How would you interpret a z score of –3.0?**

Since the z score is determined by the position of the mean and curve of the data, a negative z score means the value is below the mean. When viewing the curve, if the z score is positive, this means the variable is above the mean as the mean is set to zero (Morgan, Leech, Gloeckner, Barrett, 2020). Since the z score is also tied to the standard deviation, when evaluating a z score of -3.0 it would mean it is 3 standard deviations lower than the mean.

**(c) What percentage of scores is between a z of –2 and a z of +2? Why is this important?**

When analyzing a normal curve, the data can be divided into scores, and depending on the area being analyzed a certain percentage of scores will fall into that range. When specifically reviewing scores between a z of -2 and a z of +2 approximately 95 % of the normal curve will be taken into consideration which is important because this is how the statistical results will be calculated (Morgan, Leech, Gloeckner, Barrett, 2020). As previously discussed, since a large percentage of scores fall between a z of -2 and a z of +2 anything further skewed is extremely rare.

**D2.3.5– Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data?**

Frequency polygons should not be used if one has nominal data as there are better options to use to display nominal data. Frequency polygons connect the points between the categories and are best used with approximately normal data therefore, it would be better to use a bar chart to display nominal data (Morgan, Leech, Gloeckner, Barrett, 2020). Selecting the appropriate display for the data being analyzed is a crucial aspect of interpreting results clearly and accurately.

**References**

Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020). *IBM SPSS for Introductory Statistics*

(5th Ed.). New York, NY