8210 WK9 DISCUSSION

Response 1

Steven stoner 

RE: Discussion - Week 9

COLLAPSE

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Frankfurt-Nachmias, 2020 stated that multiple regression estimates how several independent variables affect one dependent variable.  Using the High School Long Study Data Set and SPSS Software, a multiple regression model was used to examine the relationship between a student's math identity, their math self-efficacy, and their math utility.  The High School Long Study Data Set has a mean socio-economic status of .0661.  The mean of .0661 would lead one to believe that the respondents leaned more middle class in the social class structure.

 

Research Question

Using the High School Long Study Data Set, a research question was developed using the multiple regression model.  The dependent variable is the scale of a student's mathematical identity.  The two independent variables used are the scale of a student's mathematics self-efficacy and the scale of a student's mathematical utility.  The question is essential to help teachers understand how students learn math and what should be done to help students build their math skills.  

The research question developed is: Do students' mathematical identity increase as their mathematics self-efficacy and utility increase?

The null hypothesis for the question is that a student's mathematical identity is not affected by mathematical self-efficacy and utility.

 

Multiple Regression Analysis

The multiple regression model was used to determine how a student's mathematics utility and self-efficacy would affect their mathematics identity.  Looking at Table 1, under the unstandardized coefficients, a student's mathematic self-efficacy increases for every unit, and their mathematic identity would increase by .55 units.  Also, for every unit a student's mathematic utility increases, their mathematic identity will increase by .128 units (Walden, 2016).  The significance level for both independent variables was below .05 at .001, so the null hypothesis may be rejected.  Since the null hypothesis is refected, it can be said that a student's mathematic self-efficacy and utility significantly affect a student's mathematic identity.

The effect size for a student's mathematic identity is .349, representing a medium effect; as the effect size increases, the significance increases (Wagner, 2020).  The medium effect shows that the results are meaningful as well.

 

Table 1

Multiple Regression Coefficients

 

 

Conclusion

Understanding how multiple variables can affect one aspect of a student's learning is essential.  Using the multiple regression model will allow educators to gather information on various levels and from numerous sources to create the best plans.  The test showed that self-efficacy, one's belief that they can do it, and utility, one's satisfaction with learning, can increase one's identity or how they see themselves as learners of a subject.  Understanding that is important for all learners and subjects makes the research meaningful.

References

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Sage Publications.

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Sage Publications.

Walden University, LLC. (Producer). (2016). Multiple regression [Video file]. Author.

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RESPONSE 2

Carey-Ann Thurlow 

RE: Discussion - Week 9 

COLLAPSE

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Multiple Regression

Pearson’s correlation is utilized to examine associations among variables, and allows researchers to examine how a variable changes as other variables change. Researchers use this method when examining two or more interval-ratio or continuous variables (Walden University, 2022). When examining variables using a multiple regression model, researchers pay close attention to the R-squared statistic. R-squared is an important statistic, as it displays the proportion of variability in the dependent variable that is accounted for by in the data being tested (Walden University, 2022). R-squared tells the researcher how good the predictors are at predicting the outcome variable (Walden University, 2022).

Using the Afrobarometer SPSS dataset, the following post answers the research question; ‘Does trust in the government decrease with an increase in participants’ problems with public schools and problems with public health clinics?’. The Afrobarometer research study collects information from four different regions in Africa to evaluate the values and experiences of the African people (PARN, 2022). The mean age of the individuals included in the Afrobarometer study is 37.14, and is important to consider in relation to perceptions of government trust in relation to issues participants may have had with public health and public schools.

In Table 1 (below), the adjusted R-square is slightly different than the R-square. Only 4.8% of the variability in respondents’ trust in government is explained by the combination of the two independent variables, problems with public health clinics and problems with public schools.

 

Table 1

Multiple Regression Summary of the Dependent and Independent Variables

 

The ANOVA test verifies that this model is significant with p<.001. If this model was not significant, researchers would want to take caution in interpreting it, or choosing different variables to analyze.

Table 2

ANOVA test for the Dependent and Independent Variables

 

The constant is a mathematical anchor where the regression line crosses the Y axis. This is now controlling the effects of other independent variables, where for every one unit increase in the independent variable, the dependent variable changes by the value of the unstandardized coefficient. So, for every one unit increase in problems with public schools, the value in citizen’s trust in government will decrease by.093 units, controlling for the variable problems with public health clinics.

Table 3

Standardized and Unstandardized Coefficients test for the Dependent and Independent Variables

 

Therefore, with a significance of p<.001, the data can be assessed as; problems with public schools and problems with public health clinics are significant predictors of the level of trust the respondents have in the government. In addition, researchers can determine if the association between the variables is weak, moderate or strong, based on the standardized coefficient value range of -1 to 1 (Walden University, 2022). Although, the test shows significance at p<.001, the standardized coefficients are a weak negative at -.115 and -.128.

The null hypothesis stating that there is no correlation between participants’ trust in government in relation to their perception of problems with public schools and problems with health clinics can be confidently rejected with a significance of p<.001.

References

Billings, J., (n.d.). Primary guide to research statistics: A monograph for use with ED: 8900 courses.  https://content.waldenu.edu/d1c00f22444bfb7cf79c9487accceada.html   

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G., (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

The Pan-African Research Network. (2022). Afrobarometer.  https://www.afrobarometer.org/

Walden University. (2022). Skill builders. Interpreting the results from regression models.  https://content.waldenu.edu/d1c00f22444bfb7cf79c9487accceada.html     

Leila Abouzaki 

RE: Discussion - Week 9

COLLAPSE

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In a research study, statistical significance is different from practical significance because even if the statistics of the study are justifiable, that does not guarantee practical usefulness (Warner, 2012). Multiple regression is an extension of bivariate regression by examining the effect of two or more independent variables on the dependent variable (Frankfort-Nachmias et al., 2020). A null hypothesis (Ho) is a statement that shows no difference between the population mean and some specified value which contradicts the research hypothesis (Frankfort-Nachmias et al., 2020). The Afrobarometer Dataset was examined through the SPSS Statistics software using data files that contain information the user intends to analyze (Wagner, 2020). The variables that interested me from the Afrobarometer Dataset were the respondents’ lived poverty index as it relates to problems with public health clinics and public schools because a respondent’s poverty level is an important social implication.

The Mean of the Age of the Respondents

The respondents’ reported age shows the population’s age group and whether data is normally distributed or skewed. The mean of the adult population is 37.19 implying that the sample represents an older population and indicates results may not be generalizable across all age groups. The median can be thought of as the “middle score” of the dataset which is 34 and the standard deviation is 14.594. The standard deviation identifies the gap between the mean (37.19) and 32.34% of the population which is within 1 standard deviation either way. The variance between the mean and the mode would indicate data modestly skewed to the left. Therefore, the measure of central tendency includes the mean, mode, and median which, in this scenario, are insignificant because the mean is considered the best measure of central tendency to use only if the data distribution is continuous and symmetrical. Consequently, the data on the age of the older population is skewed so the central tendency is unquantifiable to the extent that the distribution varies from a normal distribution.

Research Question

Using the Afrobarometer dataset, a research question was constructed through a correlation and bivariate regression test to find an answer. Analysis of variance (ANOVA) is inferential statistics that test the differences between mean scores of two or more groups across one or more than one variable (Wagner, 2020). The depedent variable is the respondents' lived poverty index and the two indepedent variables are problems with public schools and problems with public health clinics used to construct the research question. Understanding the poverty index can influence individuals’ problems with health clinics and public schools. Using the Afrobarometer data, the following research question and hypothesis were developed:  

· Research question: Do people with a higher lived poverty index have an increase in their problems with public health clinics and public schools? 

· The null hypothesis (Ho): There is no relationship between the lived poverty index and problems with public health clinics and public schools. 

· The alternative hypothesis (Ha): There is a relationship between the lived poverty index and problems with public health clinics and public schools. 

Analysis of the Multiple Regression

            A multiple regression test is used to determine the relationship between the two independent variables of problems with public health clinics and public schools and the independent variable of the lived poverty index. The unstandardized coefficient shows that for every problem with public health clinics, the lived poverty index will change by .035 (table 1) units controlling for problems with public schools (Walden University, 2016). Similarly, for every problem with public schools, the lived poverty index will change by .025 (table 1) units controlling for problems with public health clinics (Walden University, 2016). The significance level is less than .001 (table 1) for both predictors of the problems with public health clinics and public schools which is well below the .05 threashold and we can reject the null hypothesis that there is no relationship between lived poverty index and problems with public health clinics and public schools (Walden University, 2016). Thus, both problems with public health clinics and problems with public schools are significant predictors of respondents' lived poverty index (Walden University, 2016). Therefore, the more problems with public health clinics and public schools, the higher the respondents’ lived poverty index will be (Walden University, 2016). 

Table 1

Coefficients

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
1	(Constant)	.878	.010		87.273	.000
	Problems w/ Public Health Clinics (higher scores=more problems)	.035	.001	.189	25.019	<.001
	Problems w/ Public Schools (higher score=more problems)	.025	.001	.137	18.071	<.001
a. Dependent Variable: Lived Poverty Index (average index of 5 poverty items)

Analysis of the Strength of the Relationship Found (Effect Size)

            When the problems with public health clinics and public schools are measured in meaningful units, the difference can be interpreted by the effect size (Warner, 2012). The effect size for the lived poverty index is based on the measures for (simple and multiple) linear regression which is the R Square (R2) (entire model) for the problems with public health clinics, and it is .088 (table 2) which means there was a small effect. A higher effect size means that the research finding has practical significance, while a small effect size indicates limited practical applications (Warner, 2012). Thus, the results of the data are slightly meaningful since a small effect was found between the lived poverty index and problems with public health clinics and public schools.

Table 2

Model Summary

 

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
					R Square Change	F Change	df1	df2	Sig. F Change
1	.297a	.088	.088	.9025	.088	1322.262	2	27385	.000
a. Predictors: (Constant), Problems w/ Public Schools (higher score=more problems), Problems w/ Public Health Clinics (higher scores=more problems)

 Conclusion

            Multiple regression is used to test the simple hypotheses and to analyze an association of causality across two or more independent variables. Visual displays of data can be invaluable because it makes it easier to understand the statistical findings through visual representation. After all, research can be useful when it organizes, summarizes, and communicates information (Frankfort-Nachmias et al., 2020). Therefore, the biggest takeaways from the respondents’ poverty level index and problems with public health clinics  and public schools are whether meaningfulness exists in the test even if it is statistically significant, which in this case is slightly meaningful since a small effect was found.

References

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Sage Publications.

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Sage Publications.

Walden University, LLC. (Producer). (2016). Multiple regression [Video file]. Author.

Warner, R. M. (2012). Applied statistics from bivariate through multivariate techniques (2nd ed.). Sage Publications.

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