Background Information
The report is based on the procedure to translate a developmental psychological research question into a statistical analysis based on the behaviour of the children. They adjust to start their schooling differently where some children prosper and some of them struggles. The research report aims to detect what variables estimate and predict academic and social adjustment to the school simultaneously. This research report is an aspect of large-scale longitudinal study that tests multiple study factors. These are problems in child attention, the extent to which children are prepared for school, factors of the parents, the quality of the classroom, the academic performance and their social adjustment. Additionally, the children in the undertaken study attended on of the three various preschools prior to start school. It is a notable fact that three preschools vary vastly in their teaching philosophies forfeiting in very different teaching practices between the preschools.
The research aims to investigate the 100 samples of large longitudinal project about what early life factors might estimate two factors such as academic ability and social investment in children.
The data consists a total of 100 samples. The number of variables is 10 in this dataset. Out of these variables, 9 variables are nominal variables and only variable (Gender) is categorial in nature. However, the nominal variable is also transformed in numerical variable by levelling the values with 0 (male) and 1 (female) (Myers, Well & Lorch Jr, 2013).
The data of psychological behaviour of the students is collected from a large longitudinal project. Total 1000 participants were involved in this study. Some of the variables are gathered from the first wave or baseline. On the other hand, other variables were taken when children were in Kindergarten. For the analysis purpose, the researcher is using the data of randomly selected 100 samples. The research is carried out by SPSS 20 software. The data analysis is quantitative in nature (Bryman & Cramer, 2012). It is an experimental research design (Christensen et al., 2011).
1.The simple linear regression model is given as –
Y = β0 + β1 * X
Here, Y = dependent variable, X = independent variable, β0 = intercept, β1 = slope of the model or coefficient of the independent variable.
1.1Hypotheses:
Null hypothesis (H0): The early literacy and numeracy (Parental lit/num activities) linearly and statistically does not influence the children’s academic ability.
Alternative hypothesis (HA): The early literacy and numeracy (Parental lit/num activities) linearly and statistically does not influence the children’s academic ability.
Methodology
Note that, level of significance is assumed to be 5% here.
Here, the dependent variable is “Academic ability”, the independent variable is “Parental lit/num activities”. The value of multiple R2 and coefficient of variation is 0.09. Therefore, the predictor variable can only explain 9% variability of the dependent variable.
The ANOVA table indicates that the significant p-value is 0.02 with F-statistic = 9.648. The p-values of the model is less than 5%. The null hypothesis is rejected as the linear significant relevance is present (Schielzeth, 2010). Hence, the model is fitted good.
Not only that, the p-value of the predictor variable is 0.02 which is less than 0.05. Therefore, the predictor variable has significant linear association with dependent variable Academic activity (Montgomery, Peck & Vining, 2012). It is also found that, for 1 unit increase in “Parental lit/num activities”, the “Academic ability” increases by 1.045 units. The relationship of dependent and independent variable is found direct.
The fitting of histogram and Normal Probability Plot are not bad.
1.2.Hypotheses:
Null hypothesis (H0): The early attention problem (Measure of attention problems) linearly and statistically does not influence the children’s academic ability.
Alternative hypothesis (HA): The early attention problem (Measure of attention problems) linearly and statistically does not influence the children’s academic ability.
Note that, level of significance is assumed to be 5% here.
Here, the dependent variable is “Academic ability”, the independent variable is “Attention Problems”. The value of multiple R2 and coefficient of variation is 0.043. Therefore, the predictor variable can only explain 4.3% variability of the dependent variable.
The ANOVA table indicates that the significant p-value is 0.039 with F-statistic = 4.37. The p-values of the model is less than 5%. The null hypothesis is rejected as the linear significant relevance is present. Hence, the model is fitted good.
Not only that, the p-value of the predictor variable is 0.039 which is less than 0.05. Therefore, the predictor variable has significant linear association with dependent variable Academic activity. It is also found that, for 1 unit increase in “Attention Problems”, the “Academic ability” decreases by 0.763 units and vice versa. The association of dependent and independent variable is found reciprocal.
The fitting of histogram and Normal Probability Plot are not very bad.
2.The multiple linear regression model is given as –
Y = β0 + β1 * X1 + β2 * X2 + … + βp * Xp.
Here, Y = dependent variable, X1, X2, …, Xp = independent variables, β0 = intercept, β1, β2, …, βp = slopes of the model or the coefficients of the independent variables (Catalina, Iordache, & Caracaleanu, 2013).
Results
Hypotheses:
Null hypothesis (H0): The independent factors “Preschool”, “Gender”, “Maternal depression”, “School readiness activities”, “Family income (‘000s)” and “Kindergarten classroom quality” linearly and significantly cannot predict the dependent factor “Social adjustment problems”.
Alternative hypothesis (HA): The independent factors “Preschool”, “Gender”, “Maternal depression”, “School readiness activities”, “Family income (‘000s)” and “Kindergarten classroom quality” linearly and significantly predict the dependent factor “Social adjustment problems”.
Note that, level of significance is assumed to be 5% here.
In this case, the dependent variable is “Social adjustment problems”, the independent variables are “Preschool”, “Gender”, “Maternal depression”, “School readiness activities”, “Family income (‘000s)”, “Kindergarten classroom quality”. The value of multiple R2 and coefficient of variation is 0.077. Therefore, the predictor variable can only explain 7.7% variability of the dependent variable.
The ANOVA table indicates that the significant p-value is 0.266 with F-statistic = 1.298. The p-value is greater than 5%. Hence, the model is no at all fitted good. Therefore, it could be concluded that the null hypothesis is not rejected with 5% level of significance as the significant linear relationship is absent.
Observing the p-values of the predictor variables, it is found that the “Kindergarten classroom quality” (p-value = 0.041<0.05) is the only significant factor that influences the response variable “Social adjustment problems”. The p-values of the other variables are greater than 0.05. Therefore, the variables do not have linear significant association with the dependent variables. These variables are “Preschool”, “Gender”, “Maternal depression”, “School readiness activities” and “Family income (‘000s)”.
It is also found that, for 1 unit increase in each “Preschool”, “Gender”, “Maternal depression”, “School readiness activities”, “Family income (‘000s)” and “Kindergarten classroom quality”, the dependent factor “Social adjustment problems” respectively decreases by 4.946 units, decreases by 9.927 units, decreases by 0.54 units, decreases by 0.309 units, increases by 0.425 units and increase by 1.933 units. The association of dependent and some independent variables (Kindergarten classroom quality and family income) is direct whereas the relevance of dependent and some independent variables (Preschool, Gender, Maternal depression and School readiness activities) are found direct (Keith, 2014).
The fitting of Normal Probability Plot and fitted histogram plot are very bad.
3.The independent sample t-test determines the difference of averages of any scale variable with respect to different levels of any other ordinal, nominal or scale variables (De Winter, 2013).
Hypotheses:
Null hypothesis (H0): The average social adjustment problems of preschool 1 and 3 are statistically equal to each other.
Alternative hypothesis (HA): The average social adjustment problems of preschool 1 and 3 are not statistically equal to each other.
Note that, level of significance is assumed to be 5% here.
The averages of social adjustment problems of preschool level 1 is 39 and the averages of social adjustment level of preschool level 3 is 25.25. The p-value of the t-statistic are 0.001 and 0.000 are for equal variances and unequal variances. Both the p-values are less than 0.05, therefore, the null hypothesis of equality of two average values are rejected with 5% level of significance (Treiman, 2014).
Hence, two averages of social adjustment problems with respect to preschool 1 and 3 are different with 95% possibility.
Hypotheses:
Null hypothesis (H0): The average social adjustment problems of preschool 2 and 3 are statistically equal to each other.
Alternative hypothesis (HA): The average social adjustment problems of preschool 2 and 3 are not statistically equal to each other.
Note that, level of significance is assumed to be 5% here.
The averages of social adjustment problems of preschool level 2 is 82.93 and the averages of social adjustment level of preschool level 2 is 25.25. The p-value of the t-statistic are 0.000 and 0.000 are for equal variances and unequal variances. Both the p-values are less than 0.05, therefore, the null hypothesis of equality of two average values are rejected with 5% level of significance.
Hence, two averages of social adjustment problems with respect to preschool 2 and 3 are different with 95% possibility.
Hypotheses:
Null hypothesis (H0): The average Kindergarten classroom quality of preschool 1 and 3 are statistically equal to each other.
Alternative hypothesis (HA): The average Kindergarten classroom quality of preschool 1 and 3 are not statistically equal to each other.
Note that, level of significance is assumed to be 5% here.
The averages of Kindergarten classroom quality level of preschool level 1 is 18.26 and the averages of Kindergarten classroom quality level of preschool level 3 is 23.90. The p-value of the t-statistic are 0.000 and 0.000 are for equal variances and unequal variances. Both the p-values are less than 0.05, therefore, the null hypothesis of equality of two average values are rejected with 5% level of significance.
Hence, two averages of Kindergarten classroom quality with respect to preschool 1 and 3 are different with 95% possibility.
Hypotheses:
Null hypothesis (H0): The average Kindergarten classroom quality of preschool 2 and 3 are statistically equal to each other.
Alternative hypothesis (HA): The average Kindergarten classroom quality of preschool 2 and 3 are not statistically equal to each other.
Note that, level of significance is assumed to be 5% here.
The averages of Kindergarten classroom quality level of preschool level 2 is 19.41 and the averages of Kindergarten classroom quality level of preschool level 3 is 23.90. The p-value of the t-statistic are 0.000 and 0.000 are for equal variances and unequal variances. Both the p-values are less than 0.05, therefore, the null hypothesis of equality of two average values are rejected with 5% level of significance.
Hence, two averages of Kindergarten classroom quality with respect to preschool 2 and 3 are different with 95% possibility.
Conclusion:
The data analysis highlights the fact that the individually both the two predictors “Early literacy and numeracy” and “Attention problems” predict the response variable “Academic ability” significantly. Further, the predictive variables such as “Preschool”, “Gender”, “Family income”, “Maternal depression”, “Kindergarten Classroom quality” and “School readiness” combinedly could not predict the dependent variable “Social adjustment” of the children. Among all the dependent factors, “Kindergarten Classroom quality” can only significantly predict the dependent variable. Lastly, the social adjustment level between children whose number of preschools are 3 or others (1 and 2) are found statistically different. The quality of Kindergarten classroom of the children whose number of preschools are 3 or others (1 and 2) are found statistically different. Therefore, higher the preschool level decreases social adjustment problem and increases the Kindergarten classroom quality (Yamamoto & Holloway, 2010).
References:
Bryman, A., & Cramer, D. (2012). Quantitative data analysis with IBM SPSS 17, 18 & 19: A guide for social scientists. Routledge.
Catalina, T., Iordache, V., & Caracaleanu, B. (2013). Multiple regression model for fast prediction of the heating energy demand. Energy and Buildings, 57, 302-312.
Christensen, L. B., Johnson, B., Turner, L. A., & Christensen, L. B. (2011). Research methods, design, and analysis.
De Winter, J. C. (2013). Using the Student’s t-test with extremely small sample sizes. Practical Assessment, Research & Evaluation, 18(10).
Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modeling. Routledge.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression analysis (Vol. 821). John Wiley & Sons.
Myers, J. L., Well, A. D., & Lorch Jr, R. F. (2013). Research design and statistical analysis. Routledge.
Schielzeth, H. (2010). Simple means to improve the interpretability of regression coefficients. Methods in Ecology and Evolution, 1(2), 103-113.
Treiman, D. J. (2014). Quantitative data analysis: Doing social research to test ideas. John Wiley & Sons.
Yamamoto, Y., & Holloway, S. D. (2010). Parental expectations and children’s academic performance in sociocultural context. Educational Psychology Review, 22(3), 189-214.
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