Capstone Project 1500 to 2000 words

schools SPSS Report

Introduction

The research question is to know if there is any significant difference in the 10th grade average math and reading score. The data set has 21 variables with 64 observations each. The variables of interest are ‘10th grade average math score’ and ‘10th grade average reading score’.

Research Hypothesis

The research question is to test if there is any significant difference in the 10th grade average math score and 10th grade average reading score. The null hypothesis, Ho: there is no significant difference in the 10th grade average math score and 10th grade average reading score. This is tested against an alternative hypothesis, h1: there is a significant difference in the 10th grade average math score and 10th grade average reading score. (Gloeckner, G. W., 2019)

Analysis

The dependent variable is score which is measured by the ratio scale of measurement. The independent variable is subject which is categorised as math and reading. Since the two groups of math and reading are dependent of each other by the same participant, paired-t test can be applied here. There are a few outliers in both the data sets as evident from the boxplot. With Skewness values of 1.8 and 1.1 for average math and reading score, their distribution is approximately normal and parametric test can be applied. (Babinec, A. J., 2017)

The mean 10th grade average math score is 165.69 with a low standard deviation of 39.65. The mean 10th grade average reading score is 169.87 with a low standard deviation of 44.172. (Demidenko, E., 2019)

Descriptives
			Statistic	Std. Error
10th grade average math score	Mean	165.69	5.036
	95% Confidence Interval for Mean	Lower Bound	155.62
		Upper Bound	175.76
	5% Trimmed Mean	161.56
	Median	158.00
	Variance	1572.413
	Std. Deviation	39.654
	Minimum	114
	Maximum	331
	Range	217
	Interquartile Range	45
	Skewness	1.827	.304
	Kurtosis	4.705	.599
10th grade average reading score	Mean	169.87	5.610
	95% Confidence Interval for Mean	Lower Bound	158.65
		Upper Bound	181.09
	5% Trimmed Mean	166.83
	Median	163.50
	Variance	1951.163
	Std. Deviation	44.172
	Minimum	89
	Maximum	327
	Range	238
	Interquartile Range	58
	Skewness	1.103	.304
	Kurtosis	1.967	.599

With t(61)=-3.021, p<5%, I reject null hypothesis at 5% level of significance and conclude that there is a significant difference in the 10th grade average math score and 10th grade average reading score. (Holcomb, Z. C., 2016)

Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	10th grade average math score & 10th grade average reading score	62	.972	.000

Paired Samples Test
		Paired Differences	t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	10th grade average math score - 10th grade average reading score	-4.177	10.888	1.383	-6.942	-1.412	-3.021	61	.004

Conclusion

With t(61)=-3.021, p<5%, there is sufficient evidence to support the claim that there is a significant difference in the 10th grade average math score and 10th grade average reading score. (Ravid, R. 2019)

References

Ravid, R. (2019). Practical statistics for educators. Rowman & Littlefield Publishers.

Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.

Demidenko, E. (2019). Advanced statistics with applications in R (Vol. 392). John Wiley & Sons.

Stehlik-Barry, K., & Babinec, A. J. (2017). Data analysis with IBM SPSS statistics. Packt Publishing Ltd.

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2019). IBM SPSS for introductory statistics: Use and interpretation. Routledge.