In Part 2 Of This Assignment, You Will Describe The Relation

In Part 2 Of This Assignment You Will Describe The Relationship Betwe

In Part 2 of this assignment, you will describe the relationship between the variables in your dataset by interpreting the Scatter Plot that you have created. You will describe this relationship by answering the following questions: 1. Insert the Scatter Plot you have created into your post. 2. Describe the following characteristics of the correlation result as interpreted from the Scatter Plot you just created : - strength - direction 3. Is this a Pearson r Scatter Plot or a Spearman Rho Scatter Plot? Justify your answer. 4. Based on your interpretation of the Scatter Plot you have created, formulate a null hypothesis consistent with these results. 5. Are there outliers in this data set? How do you assess for these when interpreting a Scatter Plot? 6. What additional information do you need to determine if this correlation is statistically significant? Does the Scatter Plot provide this information? If the correlation is statistically significant, does that mean you reject or fail to reject H0?

Paper For Above instruction

The analysis of the relationship between variables through scatter plots is a fundamental aspect of understanding data in research. Interpreting such plots allows researchers to assess the strength, direction, and significance of correlations, providing insights into potential associations or causal relationships. This paper discusses the critical steps involved in analyzing a scatter plot, including how to interpret the correlation's strength and direction, determine the type of correlation, formulate hypotheses, identify outliers, and understand the necessary additional information for significance testing.

Inserting and Interpreting the Scatter Plot

The first step involves inserting the scatter plot into the research documentation. A scatter plot visually represents the relationship between two quantitative variables by plotting individual data points on a Cartesian plane. The interpretation begins by observing the overall pattern of the points. If the points cluster closely around a straight line, the correlation is considered strong; if dispersed widely, it indicates a weak correlation. The pattern's slope indicates the relationship's direction: an upward trend signifies a positive association, while a downward trend indicates a negative association.

Assessing the strength involves examining how tightly the data points cluster around the line of best fit. For strong relationships, the points are closely packed; for weak ones, they are more dispersed. The direction signifies whether variables increase together (positive) or inversely (negative). This visual assessment provides initial insights but must be supplemented with statistical measures like the correlation coefficient.

Type of Correlation: Pearson r vs. Spearman Rho

Determining whether the scatter plot represents a Pearson r or Spearman Rho correlation depends on the nature of the data and the underlying assumptions. The Pearson correlation assesses linear relationships between interval or ratio data, assuming normal distribution and homoscedasticity. In contrast, Spearman Rho evaluates monotonic relationships and is used with ordinal data or when the data do not meet parametric assumptions. Justification for this classification involves examining the data's measurement level and distribution. For instance, if the data are continuous, roughly linear, and normally distributed, the plot likely corresponds to a Pearson r plot. If the data are ranks or show nonlinear but monotonic relationships, a Spearman Rho plot is more appropriate.

Formulating the Null Hypothesis

Based on the scatter plot's interpretation, a null hypothesis (H0) typically states that there is no association between the variables. For example, H0: ρ = 0 (no correlation), or in terms of the Pearson r, H0: r = 0. This hypothesis will be tested statistically to determine if the observed correlation is significant beyond chance. The visual assessment from the scatter plot guides the initial expectation but must be confirmed with inferential statistics.

Identifying Outliers

Outliers are data points that deviate markedly from the overall pattern, potentially influencing correlation estimates. When interpreting a scatter plot, outliers appear as isolated points distant from the main cluster. Assessing outliers involves examining their impact on the data's pattern and considering whether they result from measurement error, data entry errors, or true variation. Outliers can inflate or deflate the correlation coefficient, affecting the validity of conclusions. Techniques such as standardized residuals, leverage points, or Cook’s distance can quantitatively identify influential outliers.

Additional Information for Statistical Significance

To determine if the correlation is statistically significant, additional information is necessary. This includes the sample size (n) and the calculated correlation coefficient (r or rho). Statistical tests like the Pearson correlation test or Spearman's rank correlation test compute p-values that indicate whether the observed association could have arisen by chance. The scatter plot itself provides a visual indication of potential significance but does not deliver p-values or confidence intervals. Therefore, statistical software or formulae are necessary to confirm significance.

Implications of Statistical Significance

If the correlation is statistically significant (p

In conclusion, the process of interpreting scatter plots extends beyond visual assessment. It involves careful consideration of the data type, identifying outliers, understanding the statistical context, and computing significance. These steps ensure a comprehensive interpretation of the relationship between variables, facilitating accurate scientific inference.

References

• Field, A. (2013). Discovering Statistics Using R. Sage Publications.
• Gosset, R. (1908). The probable error of a mean. Biometrika, 6(1), 1-25.
• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied statistics for the behavioral sciences. Houghton Mifflin.
• Lehmann, E. L., & D’Abrera, H. J. (2006). Nonparametrics: Statistical methods based on ranks. Princeton University Press.
• Myers, R. H. (2011). Classical and Modern Test Theory. Routledge.
• Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences. McGraw-Hill.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
• Wilkinson, L. (2012). The Grammar of Graphics. Springer.
• Zar, J. H. (2010). Biostatistical Analysis. Pearson.
• Conover, W. J. (1999). Practical Nonparametric Statistics. Wiley.