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Review a students response to D2.1 & D2.2. Summarize their findings and indicate areas of agreement, disagreement and improvement. Support your views with citations and include a reference page.

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D2.1 Working with Variables

D2.1a Compare and Contrast Nominal, Dichotomous, Ordinal, and Normal Variables

In a review of all the variables, Morgan et al. (2013) define nominal variables are defined as “three or more unordered categories” (p. 39). Moreover, Morgan et al. (2013) define dichotomous variables as “two categories, either ordered or unordered” (p. 39). Next, Morgan et al. (2013) define ordinal variables as “three ore more ordered levels” where there are unlevel distortions in the interpretation of the data, or there is inequality in the normal distribution of the data (p. 39). Last, Morgan et al. (2013) define normal variables as “many (at least five) ordered levels or scores, with the frequency distribution of the scores being approximately normal” (p. 39). When reviewing all these variables there are varying levels of importance. The first point to consider is the order of the categories. Distinctions are made between ordered levels. For example, nominal and dichotomous variables are unordered; however, dichotomous variables can also be ordered, as ordinal and normal variables must be ordered. The next component is the number of categories. All categories are multiples when reviewing variables. Dichotomous variables have two categories, nominal variables and ordinal variables have three or more categories, and normal variables have five categories.

D2.1b Distinguishing between Interval and Ratio Data in Social Science Research

In social science research, it is important to determine the differences between interval and ratio data. Morgan et al. (2013) argue, “interval variables have ordered categories that are equally spaced” (p. 42). A formidable example of interval data would be level of extroversion for a research subject. This measure is scalable but does not have a zero scale. Moreover, Morgan et al. (2013) argues, ratio variables have “a true zero” with the measurements and have equal measurements (p. 42). A formidable example of ratio data would be measurement of a research subject’s height in feet and inches.

D2.2 Understanding z Scores and the Population

In looking at z scores, these units in a normally distributed curve show the frequency distributions in one and two standard deviations of the mean. Standard deviations are also quantified or described as sigmas. Looking at the frequency of the normal curve, given normally distributed variables, the researcher can quickly identify skewness in the population. For example, if the researcher was studying the impact of mathematics scores, and a majority of the variables had a z score of +2.00; or two standard deviations (sigmas) from the frequency distribution in a normal curve, the data would be skewed to the higher end of performance and may not be meaningful for the statistical analysis of the data. Probability would tell the researcher that such high scores are abnormal, resulting in errors that need to be corrected in the data coding, or worse, potentially an error in the data collection method, which can eliminate a variable from contributing to the research analysis. Morgan et al. (2013) argue, 68% of the population should fall within one standard deviation in a normal curve probability distribution (p. 50). Large quantities of results outside of the normal frequency distribution would be classified as skewed, and must be interpreted as such, if skewed results are to be analyzed.

D2.2a z Scores and Relation to the Normal Curve

In a review of z scores for the normal curve, each z score can determine the probably that the result, or data is above or below a certain percentage. For example, a z score between zero and one would account for 34% of the frequency distribution. A z score between one and two, would be 13.5% of the population in the study. With a symmetrical curve, most of the z scores should be >-2.00 and <2.00 at 95% of the population in the study. An excess of data outside the frequency distribution may be outliers that need to be addressed with data coding. These errors should be caught in the data checking phase, as it requires rework if outliers are caught in the measurement and analysis phases.

D2.2b How to Interpret a z Score of -3.00

A z score of -3.00 would be about 1% of the normal frequency distribution of the research population, so there are two typical situations that occur when this happens. First is to determine if the score is an outlier due to error in coding. In looking at mathematics scores from 500 to say 1,000, there may be one record that is at 501 when the next score is at 550. With such a data result on the low end of the range, one result could be at the near bottom due to error in coding. The researcher must identify these issues and develop a plan to correct, omit, or keep the data as is without bias taking hold in the research analysis. The second situation is validating the data, as the result could in fact be factual. These situations with a significant number of outliers often result in the researcher asking more questions for future research, rather than obtaining answers. While limited z scores of -3 can be expected, a large frequency distribution of scores in the +3.00 or -3.00 range are a cause for concern and is something that the researcher needs to address, as these results are extremely rare.

D2.2c Percentage of Scores between a Value of -2 and +2

In establishing the percentage of scores between -2.00 and +2.00, the total value is 95% of the distribution. For the most part, in a normal curve, all the results are going to be distributed in this curve, at least with a 95% probability.

D2.2d Understanding the Importance of Percentage of Scores

It is important to understand the percentage of scores to identify skewness. Curves that are skewed, or do not follow normal frequency distributions may not follow standard scores. Morgan et al. (2013) argues “values not falling within two standard deviations of the mean are seen as relatively rare events” (p. 52).

References

Morgan, G., Leech, N., Gloeckner, G., & Barrett, K. (2013). IBM SPSS for Introductory Statistics (5th Ed.). New York, NY.