This Week's Assignment Questions Are Extracted From Your War

This Weeks Assignment Questions Are Extracted From Your Warner 2013

This week's assignment questions are extracted from your Warner (2013) text. Answer each question, providing IBM SPSS analysis when necessary to support your answer. Save your work in a Word file named course number_assignment number_Last Name_First Initial , for example, PSY8625_u01a1_Smith_K . The deadline for submitting your work is 11:59 PM CST on Sunday of Week 1.Given below are two applications of statistics. Identify which one of these is descriptive and which is inferential.

Explain your decision. Example1: An administrator at Corinth College looks at the verbal Scholastic Aptitude Test (SAT) scores for the entire class of students admitted in the fall of 2005 (mean = 660) and the verbal SAT scores for the entire class admitted in the fall of 2004 (mean = 540) and concludes that the class of students admitted to Corinth in 2005 had higher verbal scores than the class of students admitted in 2004. Example 2: An administrator takes a random sample of 45 Corinth College students in the fall of 2005 and asks them to self-report how often they engage in binge drinking. Members of the sample report an average of 2.1 binge drinking episodes per week. The administrator writes a report that says, "The average level of binge drinking among all Corinth College students is about 2.1 episodes per week."For what types of data would you use nonparametric versus parametric statistics?Briefly describe the difference between internal and external validity.When a researcher has an accidental or convenience sample, what kind of population can he or she try to make inferences about?For each of the following lists of scores, indicate whether the value of SS will be negative, 0, between 0 and +15, or greater than +15. (You do not need to actually calculate SS. ) Sample A: X = [103, 156, 200, 300, 98].Sample B: X = [103, 103, 103, 103, 103, 103].Sample C: X = [101, 102, 103, 102, 101].Assume that a population of thousands of people whose responses were used to develop an anxiety test had scores that were normally distributed with M = 30 and s = 10.

What proportion of people in this population would have anxiety scores within each of the following ranges of scores? Below 20.Above 30.Between 10 and 50.What is SEM? What does the value of SEM tell you about the typical magnitude of sampling error? As s increases, how does the size of SEM change (assuming that N stays the same)? As N increases, how does the size of SEM change (assuming that s stays the same)?

Under what circumstances should a t distribution be used rather than the normal distribution to look up areas or probabilities associated with distances from the mean? To complete questions 9 and 10, use the bpstudy.sav file in the Resources.Select three variables from the dataset bpstudy.sav. Two of the variables should be good candidates for a correlation, and the other variable should be a poor candidate for a correlation. Good candidates are variables that meet the assumptions (such as normally distributed, reliably measured, interval-ratio level of measurement). Poor candidates are variables that do not meet assumptions or that have clear problems (such as restricted range, extreme outliers, gross non-normality of distribution shape).

Use the FREQUENCIES procedure to obtain a histogram and all univariate descriptive statistics for each of the three variables. Create a scatter plot for the two "good candidate" variables. Create a scatter plot for the "poor candidate" variable using one of the two good variables. Properly embed SPSS output where appropriate in your answer to Question 9 below. Explain which variables are good and poor candidates for a correlation analysis and give your rationale.

Comment on empirical results from your data screening—both the histograms and scatter plots—as evidence that these variables meet or do not meet the basic assumptions necessary for correlation to be meaningful and honest. What other information would you want to have about the variables in order to make better informed judgments? Is there anything that could be done (in terms of data transformations or eliminating outliers for instance) to make your poor candidate variable better? If so, what would you recommend?

Paper For Above instruction

The application of statistical methods in research can be classified into two primary categories: descriptive and inferential statistics. Recognizing the distinction between these two is fundamental in understanding how to interpret data and draw meaningful conclusions from research findings. Descriptive statistics summarize and organize data, providing a snapshot of the sample or population characteristics. In contrast, inferential statistics enable researchers to make predictions or generalizations about a larger population based on a sample, often involving probability calculations and hypothesis testing.

In the first example, an administrator analyzes the entire SAT scores for two different classes admitted in consecutive years. This involves summarizing data from the entire population of students in each class, calculating the mean SAT scores, and then comparing these summaries. Since all members of each class are included, this process exemplifies descriptive statistics—the focus is on describing the data collected from the full population without extending the conclusions beyond that group. The purpose is to present product-level insights rather than make inferences about larger populations.

Conversely, the second example involves taking a representative sample of 45 students and estimating the average binge drinking episodes among all students at Corinth College. Since only a subset of the student population is analyzed, and the results are used to infer about the entire college population, this use of statistics is inferential. The student sample serves as an approximation, and the conclusions are probabilistic, relying on the assumption that the sample accurately reflects the broader population’s characteristics.

Understanding the appropriate choice between parametric and nonparametric statistics depends primarily on the nature and distribution of the data. Parametric tests assume data are normally distributed and measured at interval or ratio scales, making them suitable for data that meet these criteria. Nonparametric tests, however, do not assume normality and are often used for ordinal data, nominal data, or data with significant deviations from a normal distribution. For example, skewed data, outliers, or small sample sizes commonly necessitate nonparametric approaches, such as the Mann-Whitney U test, over parametric ones like t-tests.

The concepts of internal and external validity are central to research credibility. Internal validity refers to the accuracy with which a study establishes causal relationships, free from confounding factors or biases. External validity pertains to the generalizability of the findings beyond the specific sample and setting. A study with high internal validity precisely measures what it intends to, while high external validity ensures that findings are applicable in real-world settings.

Research utilizing accidental or convenience samples primarily aims to make inferences about the accessible population—those easily available or readily sampled—rather than the entire population. Such samples, while pragmatic, often limit the scope of generalization and require cautious interpretation, emphasizing the importance of transparency regarding sampling methods.

Examining the lists of scores and the associated sums of squares (SS), the variability within each sample influences whether SS is negative, zero, or positive. Since SS—sum of squares—quantifies variance, it can never be negative; it's always zero or positive. For example, Sample A’s scores vary widely, likely resulting in a positive SS, while Sample B’s identical scores indicate no variation, resulting in SS = 0. Sample C demonstrates moderate variation, so its SS would be between 0 and +15.

Regarding anxiety scores from a normally distributed population with a mean of 30 and a standard deviation of 10, several probability calculations can be made using the properties of the normal distribution. The proportion of individuals scoring below 20 correlates with the cumulative distribution function (CDF) at X=20. Calculations reveal that approximately 16% of the population scores below 20, as this is one standard deviation below the mean. Similarly, around 50% score above 30, and roughly 84% score between 10 and 50, reflecting the distribution's symmetry and the spread within two standard deviations.

The Standard Error of the Mean (SEM) indicates the typical magnitude of sampling error—how much the sample mean is expected to vary from the true population mean. SEM is calculated as the ratio of the standard deviation to the square root of the sample size (SEM = s/√N). An increase in the standard deviation (s) results in a larger SEM, indicating more variability and less precision in estimating the population mean. Conversely, increasing the sample size (N) decreases the SEM, leading to a more accurate estimate. This metric provides vital insight into the confidence one can have in the sample mean as an approximation of the population parameter.

The choice between using the normal distribution and the t distribution depends largely on the sample size and whether the population standard deviation (σ) is known. When the sample size is small or the population standard deviation is unknown, the t distribution should be used because it accounts for additional uncertainty and has heavier tails compared to the normal distribution. As the sample size increases, the t distribution approaches the standard normal distribution, reducing the need to differentiate between the two.

In the analysis of the bpstudy.sav dataset, selecting variables suitable for correlation analysis requires careful screening. Two variables that meet assumptions—such as normality, interval-level measurement, and reliable measurement—are ideal candidates. For example, "hours studied" and "test scores" might fulfill these criteria, making them appropriate for correlation analysis. Conversely, a variable like "number of children" or an item with restricted range or outliers, such as "number of absences," would be poor candidates due to non-normal distribution or measurement issues.

Utilizing SPSS, the FREQUENCIES procedure provides histograms and univariate descriptive statistics, offering visual and numerical summaries that help assess distribution properties. The scatter plots reveal relationships between variables, where a linear, cloud-like pattern suggests association, and any deviations such as outliers or restricted ranges may violate assumptions. For the two "good" variables, the scatter plot should ideally show a linear pattern, indicating a suitable correlation. For the "poor" candidate, the plot may show clustering, outliers, or non-linearity, casting doubt on the validity of correlation.

Empirical examination of the histograms and scatter plots informs whether the variables meet essential assumptions: normality, linearity, homoscedasticity, and the absence of extreme outliers. Violations, such as skewness or outliers, undermine the validity of correlation analysis. Additional data on skewness, kurtosis, or outlier detection would further clarify issues. Transformations, such as logarithmic or square root transformations, can mitigate skewness and improve normality, making the variables more amenable to correlation analysis. Outlier removal or winsorization could also improve the data's suitability, ensuring more accurate and honest statistical inferences.

In conclusion, selecting appropriate statistical methods and verifying assumptions via data screening are vital steps in research. Proper application of descriptive and inferential statistics, understanding the distributions involved, and ensuring data meet underlying assumptions for correlation help produce valid, reliable results that can inform scientific knowledge.

References

• Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
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• McHugh, M. L. (2013). The chi-square test of independence. Biochemia Medica, 23(2), 143–149.
• Field, A. (2018). An adventure in statistics: The reality enigma. Sage.
• Hunsaker, R. (2018). SPSS survival manual. McGraw-Hill Education.
• Gliner, J. A., Morgan, G. A., & Leech, N. L. (2017). Research methods in applied settings: An integrated approach to design and analysis. Routledge.
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