Read Morgan Leech Gloeckner Barrett Chapter 3 Page Read Kell

Read Morgan Leech Gloeckner Barrett Chapter 3pageread Keller

Read Morgan Leech Gloeckner Barrett Chapter 3; Read Keller; Watch: Introduction to Descriptive Statistics

DISCUSSION ASSIGNMENT INSTRUCTIONS: The student will complete Integrating Faith and Learning discussion. In the thread for each short-answer discussion, the student will post short answers to the prompted questions. The answers must demonstrate course-related knowledge and support their assertions with scholarly citations in the latest APA format. Minimum word count for all short answers cumulatively is 200 words. The minimum word count for Integrating Faith and Learning discussion is 600 words.

For each thread, the student must include a title block with your name, class title, date, and the discussion forum number; write the question number and the question title as a level one heading (e.g., D1.1 Variables) and then provide your response; use Level Two headings for multi-part questions (e.g., D1.1 & D1.1.a, D1.1.b, etc.), and include a reference section. The student must then post one reply to another student’s post. 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 a corresponding list of references. The minimum word count for the reply is 250 words. Discussion Thread: Variables, Z Scores, Population and Output Respond to the following short-answer questions from Chapter Three in the Morgan, Leech, Gloeckner, & Barrett textbook: If you have categorical, ordered data (such as low income, middle income, high income), what type of measurement would you have? Why? 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? D2.3.3. 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? D2.3.4. (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? D2.3.5. Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data?

Paper For Above instruction

Understanding measurement levels and statistical concepts is essential in social science research, as it influences how data is collected, analyzed, and interpreted. This essay explores various measurement types, the significance of distinguishing between different variable levels, properties of the normal curve, and appropriate data visualization techniques, integrating insights from Morgan, Leech, Gloeckner, & Barrett (2019), Keller (2019), and foundational statistical principles.

Measurement of Ordered Categorical Data

Categorical, ordered data, like income levels categorized as low, middle, and high, are best measured using ordinal measurement. Ordinal data possess a clear ranking or order but do not quantify the magnitude of differences between categories (Morgan et al., 2019). Such data indicate relative standing but lack precise intervals, making ordinal measurement suitable. For example, income categories reflect relative socioeconomic status, but the distance between 'low' and 'middle' income is not necessarily equal to that between 'middle' and 'high'.

Comparison of Variable Types and Their Significance

(a) Nominal variables are categorical without inherent order—for instance, gender or race. Dichotomous variables are a type of nominal variable with only two categories, such as yes/no responses. Ordinal variables, as described, involve ranking but not equal intervals—such as education level (high school, college, graduate). Normal variables, more accurately termed continuous variables that are assumed to follow a normal distribution, often relate to interval or ratio scales, which have equal intervals and an absolute zero, respectively (Morgan et al., 2019).

(b) In social science research, distinguishing strictly between interval and ratio variables is sometimes less critical because many statistical tests are robust across these scales. Both are continuous, with ratio variables having an absolute zero point, enabling ratio comparisons. However, many analyses treat them similarly due to their shared continuous nature, emphasizing the distinction less critical for certain descriptive and inferential purposes (Keller, 2019).

Properties of the Standard Normal Distribution

Approximately 68% of the area under the standard normal curve lies within one standard deviation of the mean, covering scores from z = –1 to z = +1 (Morgan et al., 2019). This indicates that most scores cluster near the mean. Scores more than one standard deviation away (less than –1 or greater than +1) are less common and considered atypical or extreme, often warranting further investigation for potential outliers or special cases.

Z Scores and Their Interpretation

(a) Z scores represent how many standard deviations a particular score is from the mean, standardizing different data points to a common scale aligned to the normal distribution (Morgan et al., 2019). This enables comparisons across different datasets or variables.

(b) A z score of –3.0 indicates that the data point is three standard deviations below the mean, representing an unusually low score. Such values are rare, occurring approximately in 0.13% of the population, and may indicate outliers or measurement errors (Keller, 2019).

(c) The percentage of scores between z = –2 and z = +2 in a normal distribution is about 95%, reflecting the empirical rule. Recognizing this range helps researchers understand the expected variability in data and identify scores that fall outside typical bounds, which may be important for detecting anomalies or extreme cases.

Visualizing Nominal Data

Frequency polygons are unsuitable for nominal data because they rely on ordered, numerical axes to depict changes across intervals; nominal data lack inherent order or numerical value (Morgan et al., 2019). Bar charts are better suited for nominal data, as they display categories clearly and facilitate comparison of frequencies without implying a numerical or ordered relationship.

Conclusion

In sum, understanding the nature of data and the appropriate statistical tools enhances the accuracy of research findings. Recognizing measurement levels, distribution properties, and visualization techniques ensures meaningful analysis, especially when integrating faith and learning perspectives that emphasize ethical data handling and honest reporting.

References

• Keller, G. (2019). Statistics for social sciences. New York, NY: Academic Press.
• Morgan, G. Leech, Gloeckner, R., & Barrett, K. (2019). IBM SPSS for introductory statistics. Routledge.