Comparative Analysis of Mathematics Scores, Science Scores, and Scholastic Assessment Test Scores

Subject: Sciences
Pages: 15
Words: 4884
Reading time:
22 min
Study level: PhD

Introduction

The academic performance of students is central in an education system because it indicates the outcome of teaching and learning processes in schools and colleges. Yearly, teachers and parents strive to equip students with the necessary knowledge and skills so that they can perform well in their exams. Despite the efforts of parents and teachers, disproportionate performance occurs among students. The academic performance of students varies from one school to another, depending on the availability of learning resources, the nature of teaching methods, and social factors that are present in the learning environment.

In only 3 hours we’ll deliver a custom Comparative Analysis of Mathematics Scores, Science Scores, and Scholastic Assessment Test Scores essay written 100% from scratch Get help

Moreover, disproportionate academic performance occurs within a school due to the existence of demographic factors, which influence how students perform in schools. For example, male students are good in certain subjects, while female students are good in certain subjects. Academic performance among students also varies according to their racial backgrounds. The gendered and racial academic performances show that learning among students follows different patterns and processes, which require theories and models to elucidate.

Education experts have cited many factors that influence learning among students and thus they have come up with learning theories, which are applicable in teaching. In essence, myriad factors mediate academic performance and learning among students in various schools. Therefore, the research paper compares the academic performance of students in terms of mathematics scores, science scores, and scholastic assessment test (SAT) scores, and establishes their relationships with gender and race.

Problem Statement

Poor academic performance is an issue that an education system, teachers, parents, and students struggle to eliminate in learning institutions. The education systems across the world spend billions of dollars in developing appropriate curricula and implementing them effectively to achieve desired goals. In the same manner, teachers are putting extra effort into their teaching programs so that students could perform well in their exams and pursue careers of interest. As parents bear the burden of parenting and schooling, they closely monitor the academic progress of their children with a view of guiding them on how to build their careers.

Likewise, students attend their classes daily and spend ample time reading to gain appropriate knowledge and skills, which would enable them to identify their talents and build their careers, and thus become successful people in society. Evidently, academic performance is a parameter, which measures outcomes of teaching and learning in schools.

In American schools and colleges, academic performance has been a significant issue in the recent past due to poor performance among students. Among 12th graders, mathematics, and sciences are the subjects in which students perform disproportionately. Moreover, SAT exams, which are essential in assessing the reading, writing, and numerical capacities of students, have caused the disproportionate entry of students into colleges.

The disproportionate academic performance in mathematics, science and SAT exams among 12th graders begs many questions. Comparative analysis of the relationships that exist among mathematics scores, science scores, and SAT scores provides insights into the factors that influence academic performance among students. Therefore, there is an urgent need to establish the relationships that exist among mathematics scores, science scores, and SAT scores in relation to gender and race.

Academic experts
available
We will write a custom Sciences essay specifically for you for only $16.00 $11/page Learn more

Objective of Research

  1. To find out if science scores and SAT scores vary significantly between male and female students.
  2. To establish if mathematics scores, science scores, and SAT scores vary significantly among White American, African American, Hispanic, and Latino students.
  3. To find the nature of correlation that exists between mathematics scores and SAT scores.

Hypotheses

The Null Hypotheses

  • H0: The performance of male and female students does not differ significantly in mathematics, science, and SAT exams.
  • H0: The White American, African American, Hispanic, and Latino students do not exhibit significant differences in mathematics scores, science scores, and SAT scores.
  • H0: Positive correlation does not exist between mathematics scores and SAT scores.

The Alternative Hypotheses

  • H1: The performance of male and female students differs significantly in mathematics, science, and SAT exams.
  • H1: The White American, African American, Hispanic, and Latino students exhibit significant differences in mathematics scores, science scores, and SAT scores.
  • H1: Positive correlation exists between mathematics scores and SAT scores.

Variables of the Study

As the study examines the academic performance of students, its variables are gender, race, mathematics scores, science scores, and SAT scores. Gender and race are independent variables of the study, while mathematics scores, science scores, and SAT scores are dependent variables. Gender is a demographic variable in the study, which is important in testing the existence of gendered performance. The race is a pertinent independent variable that helps in establishing the existence of disproportionate performance of students owing to their races. In this view, the study examines White American, African American, Hispanic, and Latino students with the objective of finding out if their academic performances differ significantly. Thus, gender and race are two independent variables that represent demographic variables, which influence academic performance among students in schools and colleges.

Mathematics scores, which form a dependent variable, are the scores of the 12th graders. The study collected mathematics scores from students, who completed their 12th-grade exams. Moreover, the study collected data on science scores from students, who completed their 12th-grade exams. Science scores form an integral dependent variable that indicates the performance of students in the 12th grade. Given that SAT scores relate to the 12th-grade exams, they are applicable in establishing the correlation relationships. Correlation analysis of mathematics and SAT scores is necessary for the study. The correlation value would indicate if mathematics scores determine SAT scores, and thus form the basis of using SAT in various colleges as an aptitude test for placement of students.

Factitious Data

The table below summarizes data collected from 40 students (N =40) with equal representation of gender (Male = 20, Female = 20). The study also balanced the participants in terms of their racial backgrounds because the White Americans, African Americans, Hispanics, and Latinos were represented by eight students (n = 8).

Table 1.

Case Summaries
Case Number Race of Students Mathematics Scores for 12th Graders Science Scores for 12th Graders SAT Scores Gender of Students
1 1 White American 72 86 700 Male
2 2 White American 62 85 725 Male
3 3 White American 75 75 680 Male
4 4 White American 80 74 659 Male
5 5 White American 95 62 692 Female
6 6 White American 83 78 726 Female
7 7 White American 69 75 653 Female
8 8 White American 82 84 625 Female
9 9 African American 78 79 702 Male
10 10 African American 82 63 560 Male
11 11 African American 56 56 640 Male
12 12 African American 64 68 580 Male
13 13 African American 65 65 520 Female
14 14 African American 52 64 623 Female
15 15 African American 49 69 536 Female
16 16 African American 75 76 573 Female
17 17 Hispanic 68 79 650 Male
18 18 Hispanic 71 81 653 Male
19 19 Hispanic 72 79 681 Male
20 20 Hispanic 73 76 702 Male
21 21 Hispanic 76 72 669 Female
22 22 Hispanic 75 75 632 Female
23 23 Hispanic 70 76 645 Female
24 24 Hispanic 78 74 663 Female
25 25 Latino 53 56 520 Male
26 26 Latino 48 62 450 Male
27 27 Latino 56 63 470 Male
28 28 Latino 52 56 380 Male
29 29 Latino 53 54 469 Female
30 30 Latino 54 58 473 Female
31 31 Latino 85 57 498 Female
32 32 Latino 46 56 502 Female
33 33 Asian 95 98 780 Male
34 34 Asian 88 95 720 Male
35 35 Asian 86 93 723 Male
36 36 Asian 84 93 760 Male
37 37 Asian 85 96 736 Female
38 38 Asian 87 98 690 Female
39 39 Asian 86 89 706 Female
40 40 Asian 89 92 715 Female
Total N 40 40 40 40 40

Data Analysis

Descriptive Statistics

The table below shows the descriptive statistics of mathematics scores, science scores, and SAT scores of the 12th graders. The descriptive statistics provide measures of central tendency and measures of dispersion and thus summarize the data for further analysis.

Table 2.

Statistics
Mathematics Scores for 12th Graders Science Scores for 12th Graders SAT Scores
N Valid 40 40 40
Missing 0 0 0
Mean 71.73 74.68 627.03
Std. Error of Mean 2.205 2.098 15.607
Median 74.00 75.00 653.00
Mode 75 56 520
Std. Deviation 13.943 13.269 98.705
Variance 194.410 176.071 9742.589
Skewness -.301 .149 -.721
Std. Error of Skewness .374 .374 .374
Kurtosis -1.013 -1.004 -.415
Std. Error of Kurtosis .733 .733 .733
Range 49 44 400
Minimum 46 54 380
Maximum 95 98 780
Sum 2869 2987 25081

The measures of central tendency that the descriptive table depicts are mean, mode, and median. For mathematics scores, the mean, mode, and median are 71.73, 75, and 74 respectively. The measures of central tendency of science scores are 74.64, 56, and 75 for mean, mode, and median respectively. Likewise, the mean, mode, and median for SAT scores are 627.03, 520, and 653 respectively. From the descriptive statistics, it is evident that measures of central tendency for mathematics scores and science scores are closer to the central measures than SAT scores. Hence, measures of central tendency are important because they depict the distribution of data, which form the basis of making inferential statistics.

15% OFF Get your very first custom-written academic paper with 15% off Get discount

Measures of dispersion are important descriptive statistics as they provide the extent to which a given data disperse from a certain central measure (Kirk, 2006). In the descriptive table, the measures of dispersion are range, variance, and standard deviation. For mathematics scores the range, variance, and standard deviation are 44, 194.41, and13.943 are respectively. Similarly, the range, variance, and standard deviation for science scores are 44, 176.07, and 13.27 respectively. The measures of dispersion for SAT scores are 400, 9742.86, and 98.71 for the range, variance, and standard deviation correspondingly. These descriptive statistics indicate that mathematics scores and science scores have similar dispersion, while SAT scores exhibit the highest degree of dispersion.

Analysis of descriptive statistics requires examination of measures of central tendency and measures of dispersion for they are inseparable in making inferences. Kirk (2006) states that the combination of a measure of central tendencies such as standard deviation and a measure of dispersion like mean provides a clear view of how descriptive statistics summarize data. For mathematics, the scores have a small variation from the mean (M = 71.3, SD = 13.943).

Likewise, sciences have small variation from the mean (M = 74.64, SD = 13.27). However, the variation in the SAT scores is huge as indicated by the standard deviation (M = 627.03, SD = 98.71). In this view, descriptive statistics are essential as they summarize data, and therefore, they provide the basis for making inferential statistics and performing further statistical analyses.

Mathematics score for 12th Graders

The histogram in figure 1 shows the distribution of mathematics scores among the 12th graders. The distribution is close to the normal distribution because most scores are close to the mean, mode, and median. Skewness and kurtosis are two statistical tests that researchers apply to determine the distribution of data. According to Ott and Longnecker (2008), skewness depicts symmetry of the distribution curve, while kurtosis shows the peakedness of the distribution curve.

The distribution curve of the mathematics scores has a negative skew of 0.301, which means the scores have a slight skew of distribution towards the right when compared to the normal distribution. Regarding kurtosis, the mathematics scores have a negative kurtosis of 1.013, which implies that they have a flatter peak than the normal distribution. Thus, the skewness and kurtosis of the mathematics scores do not deviate significantly from the normal distribution. In this view, the data meets the assumption of the normal distribution, which various statistical tests require.

Science score for 12th Graders

Get your customised and 100% plagiarism-free paper on any subject done for only $16.00 $11/page Let us help you

Figure 2 is a histogram, which exhibits the distribution of science scores among the 12th-grade students. Ott and Longnecker (2008) state the values of skewness and kurtosis are zero in a normal distribution curve. The skewness of the distribution is positive 0.149, which means that its distribution skews towards the left. Since the skewness value of the distribution is close to zero, it follows that of the normal distribution curve. Moreover, the distribution curve has a negative kurtosis of 1.004. The negative kurtosis implies that the peakedness of science scores is below that of the normal distribution. Given that the skewness and kurtosis values are within the close range of the normal distribution curve, the science scores follow the normal distribution and thus meet the assumptions of the tests like correlation, analysis of variance, t-test, and chi-square test amongst others.

SAT Scores

Figure 3 shows the distribution table of SAT scores of students. Examination of skewness and kurtosis of the distribution indicates how the distribution curve varies from the normal distribution curve. Apparently, the distribution curve has a negative skew because it skews towards the right side. Ott and Longnecker (2008) state that the distribution curve that skews towards the right side is negative, while the one that skews towards the left is positive. From the descriptive table, the skewness is negative 0.721. The skewness value is very high as it depicts that over half of students have scored the highest scores. Concerning the kurtosis, the distribution table has a positive value of 0.733. This value of kurtosis indicates that the peakedness of the distribution curve is greater than that of a normal curve.

Hypothesis Testing: Statistical Tests

The First Hypothesis

H0: The performance of male and female students does not differ significantly in mathematics, science, and SAT exams.

The data for testing this hypothesis fit that of one-way ANOVA. The data for the analysis of one-way ANOVA meet the following assumptions.

  1. The dependent variables, which are mathematics scores, science scores, and SAT scores, are in a continuous form.
  2. The independent variable, which is gender, comprises two categories, male and female students.
  3. The scores of mathematics, science and SAT are quite independent of each other and gender.
  4. The scores of mathematics, science and SAT have no significant outliers.
  5. The distribution of scores for mathematics, science, and SAT is close to normal distribution.

Gender and Mathematics Performance

Table 3.

ANOVA
Mathematics Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 38.025 1 38.025 .192 .664
Within Groups 7543.950 38 198.525
Total 7581.975 39

From the ANOVA table, it is evident that the performance of male and female students in mathematics does not differ significantly at the significance level of p<0.05, [F (1, 38) = 0.192, p = 0.664]. In this view, the test fails to reject the null hypothesis, which holds that gender does not influence the performance of students in mathematics.

Gender and Science Performance

Table 4.

ANOVA
Science Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 55.225 1 55.225 .308 .582
Within Groups 6811.550 38 179.251
Total 6866.775 39

The ANOVA table shows that the science scores do not differ significantly between male and female students at a significance level of p<0.05 [F (1, 38) = 0.308, p = 0.582]. This test fails to reject the null hypothesis, and thus the null hypothesis still holds that gender does not influence the performance of students in science.

Gender and SAT Performance

Table 5.

ANOVA
SAT Scores
Sum of Squares df Mean Square F Sig.
Between Groups 3783.025 1 3783.025 .382 .540
Within Groups 376177.950 38 9899.420
Total 379960.975 39

The ANOVA table shows that gender does not have a significant influence on SAT scores among students at the significance level of p<0.05 [F (1, 38) = 0.382, p = 0.540]. Since the p-value is insignificant, it implies that the null hypothesis, which states that the performance of students in terms of SAT scores does not differ significantly between male and female students, still holds.

Combined Analysis

Table 6.

ANOVA
Sum of Squares df Mean Square F Sig.
SAT Scores Between Groups 3783.025 1 3783.025 .382 .540
Within Groups 376177.950 38 9899.420
Total 379960.975 39
Mathematics Scores for 12th Graders Between Groups 38.025 1 38.025 .192 .664
Within Groups 7543.950 38 198.525
Total 7581.975 39
Science Scores for 12th Graders Between Groups 55.225 1 55.225 .308 .582
Within Groups 6811.550 38 179.251
Total 6866.775 39

Decision

Based on the ANOVA table, the test fails to reject the null hypothesis because the p-value is greater than the significance level of 0.05. Jackson (2011) states that the p-value must be less than 0.05 or a specific significance level for it to be significant. Thus, the performance of male and female students does not differ significantly in mathematics, science, and SAT exams because the test values are [F (1, 38) = 0.192, p = 0.664], [F (1, 38) = 0.308, p = 0.582], and [(F (1, 38) = 0.382, p = 0.540] respectively. Therefore, the hypothesis test shows that the performance of students in mathematics, science, and SAT does not vary according to the gender of the students

The Second Hypothesis

H0: The White American, African American, Hispanic, and Latino students do not exhibit significant differences in mathematics, science, and SAT scores.

The appropriate tests of this hypothesis are one-way ANOVA and post hoc analysis. These tests are appropriate because the data meet the following assumptions.

  1. The dependent variables, which are mathematics scores, science scores, and Sat scores, are in a continuous form.
  2. The independent variable, which is race, comprises four categories.
  3. The scores of mathematics, science and SAT are quite independent of each other and race.
  4. The scores of mathematics, science and SAT have no significant outliers.
  5. The distribution of scores for mathematics, science, and SAT follows the normal distribution.
  6. The independent variable, race, has more than two categories, and thus requires post hoc analysis.

Race and Mathematics Performance

Table 7.

ANOVA
Mathematics Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 4603.850 4 1150.963 13.527 .000
Within Groups 2978.125 35 85.089
Total 7581.975 39

The ANOVA table indicates that White American, African American, Hispanic, and Latino students exhibit a significant difference in mathematics scores at a significance level of 0.05 [F (4, 35) = 13.527, p = 0.000]. Thus, the test rejects the null hypothesis, which holds that mathematics performance does not vary according to the race of students.

Since there are four independent variables, comparative analysis of two variables exhibits some internal variations. Post hoc analysis shows that mathematics scores significantly vary among students of all races except for Hispanic and White American students and Hispanic and African Americans because their p-values are 0.379 and 0.102 respectively, which are insignificant.

Table 8.

Multiple Comparisons
Dependent Variable: Mathematics Scores for 12th Graders
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 12.125* 4.612 .013 2.76 21.49
Hispanic 4.375 4.612 .349 -4.99 13.74
Latino 21.375* 4.612 .000 12.01 30.74
Asian -10.250* 4.612 .033 -19.61 -.89
African American White American -12.125* 4.612 .013 -21.49 -2.76
Hispanic -7.750 4.612 .102 -17.11 1.61
Latino 9.250 4.612 .053 -.11 18.61
Asian -22.375* 4.612 .000 -31.74 -13.01
Hispanic White American -4.375 4.612 .349 -13.74 4.99
African American 7.750 4.612 .102 -1.61 17.11
Latino 17.000* 4.612 .001 7.64 26.36
Asian -14.625* 4.612 .003 -23.99 -5.26
Latino White American -21.375* 4.612 .000 -30.74 -12.01
African American -9.250 4.612 .053 -18.61 .11
Hispanic -17.000* 4.612 .001 -26.36 -7.64
Asian -31.625* 4.612 .000 -40.99 -22.26
Asian White American 10.250* 4.612 .033 .89 19.61
African American 22.375* 4.612 .000 13.01 31.74
Hispanic 14.625* 4.612 .003 5.26 23.99
Latino 31.625* 4.612 .000 22.26 40.99

Race and Science Performance

Table 9.

ANOVA
Science Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 5853.900 4 1463.475 50.571 .000
Within Groups 1012.875 35 28.939
Total 6866.775 39

From the ANOVA table, it is evident that there are significant differences in math scores among students according to their races at a significant level of 0.05 [F (4, 35) = 50.571, p = 0.000]. This test, therefore, rejects the null hypothesis and accepts the alternative one, which holds that science scores vary according to different races.

Post hoc analysis shows that significant differences exist between scores of two races except for the White and Hispanic students, which do not have significant differences because the p-value is greater than the significance value.

Table 10.

Multiple Comparisons
Dependent Variable: Science Scores for 12th Graders
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 9.875* 2.690 .001 4.41 15.34
Hispanic .875 2.690 .747 -4.59 6.34
Latino 19.625* 2.690 .000 14.16 25.09
Asian -16.875* 2.690 .000 -22.34 -11.41
African American White American -9.875* 2.690 .001 -15.34 -4.41
Hispanic -9.000* 2.690 .002 -14.46 -3.54
Latino 9.750* 2.690 .001 4.29 15.21
Asian -26.750* 2.690 .000 -32.21 -21.29
Hispanic White American -.875 2.690 .747 -6.34 4.59
African American 9.000* 2.690 .002 3.54 14.46
Latino 18.750* 2.690 .000 13.29 24.21
Asian -17.750* 2.690 .000 -23.21 -12.29
Latino White American -19.625* 2.690 .000 -25.09 -14.16
African American -9.750* 2.690 .001 -15.21 -4.29
Hispanic -18.750* 2.690 .000 -24.21 -13.29
Asian -36.500* 2.690 .000 -41.96 -31.04
Asian White American 16.875* 2.690 .000 11.41 22.34
African American 26.750* 2.690 .000 21.29 32.21
Hispanic 17.750* 2.690 .000 12.29 23.21
Latino 36.500* 2.690 .000 31.04 41.96

Race and SAT Performance

Table 11.

ANOVA
SAT Scores
Sum of Squares df Mean Square F Sig.
Between Groups 323701.600 4 80925.400 50.345 .000
Within Groups 56259.375 35 1607.411
Total 379960.975 39

According to the ANOVA tables, at a significant level of 0.05, students exhibit significant differences in SAT scores according to their races [F (4, 35) = 50.345, p = 0.000]. Hence, the test rejects the null hypothesis and accepts the alternative one, which supports that SAT scores differ significantly among students from different races.

Post hoc analysis shows that significant interracial variation exists in the SAT scores except between the White American and Hispanic students. The p-value of the variation between African American and Hispanic students is 0.311, which is quite insignificant.

Table 12.

Multiple Comparisons
Dependent Variable: SAT Scores
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 90.750* 20.046 .000 50.05 131.45
Hispanic 20.625 20.046 .311 -20.07 61.32
Latino 212.250* 20.046 .000 171.55 252.95
Asian -46.250* 20.046 .027 -86.95 -5.55
African American White American -90.750* 20.046 .000 -131.45 -50.05
Hispanic -70.125* 20.046 .001 -110.82 -29.43
Latino 121.500* 20.046 .000 80.80 162.20
Asian -137.000* 20.046 .000 -177.70 -96.30
Hispanic White American -20.625 20.046 .311 -61.32 20.07
African American 70.125* 20.046 .001 29.43 110.82
Latino 191.625* 20.046 .000 150.93 232.32
Asian -66.875* 20.046 .002 -107.57 -26.18
Latino White American -212.250* 20.046 .000 -252.95 -171.55
African American -121.500* 20.046 .000 -162.20 -80.80
Hispanic -191.625* 20.046 .000 -232.32 -150.93
Asian -258.500* 20.046 .000 -299.20 -217.80
Asian White American 46.250* 20.046 .027 5.55 86.95
African American 137.000* 20.046 .000 96.30 177.70
Hispanic 66.875* 20.046 .002 26.18 107.57
Latino 258.500* 20.046 .000 217.80 299.20

Decision

The ANOVA test and post hoc analysis indicates that variation is mathematics score, science scores, and SAT scores differ significantly across students of different races. Since the p-value is less than 0.05, the test, therefore, rejects the null hypothesis and accepts the alternative one, which states that the White American, African American, Hispanic, and Latino students do exhibit significant differences in mathematics, science, and SAT scores.

The Third Hypothesis

H0: Positive correlation does not exist between mathematics scores and SAT scores.

The data meet the assumptions of correlation analysis because mathematics scores and SAT scores are continuous variables, the linear relationships, and they do not have significant outliers.

Table 13.

Correlations
Mathematics Scores for 12th Graders SAT Scores
Mathematics Scores for 12th Graders Pearson Correlation 1 .726
Sig. (2-tailed) .000
N 40 40
SAT Scores Pearson Correlation .726 1
Sig. (2-tailed) .000
N 40 40

The correlation table shows that a significant correlation exists between mathematics scores and SAT scores, r(38) = 0.726, p<0.05. According to Weinberg and Abramowitz (2008), a strong and positive correlation ranges from 0.7 to 1.0. Hence, since the correlation value is 0.726, it is very strong and positive, while the p-value is 0.000, which is very significant. In this view, the Pearson correlation test rejects the null hypothesis because the correlation value is very significant.

Decision

Therefore, the correlation test rejects the null hypothesis and accepts the alternative one, which states that a positive correlation exists between mathematics scores and SAT scores.

Conclusion

The comparative analysis of mathematics scores, science scores, and SAT scores in relation to gender and race provides invaluable information about the performance of students. The ANOVA analysis of different scores for mathematics, science, and SAT in relation to gender indicates that they have no significant differences. In contrast, analysis of mathematics scores, science scores, and SAT scores in relation to race depicts that the scores significantly vary according to the race of students. Moreover, correlation analysis shows that mathematics scores and SAT scores have a significant correlation.

Thus, the ANOVA results indicate that male and female students have similar performances in mathematics, science, and SAT. However, the ANOVA results show that students from various races have exhibited different performances in mathematics, science, and SAT. This implies that education experts need to identify factors that contribute to racial performance. Regarding correlation, the findings show that mathematics scores correlate with SAT scores, and hence, as mathematics precedes SAT scores, it influences SAT scores among students.

References

Jackson, S. (2011). Research Methods and Statistics: A Critical Thinking Approach. New York: Cengage Learning.

Kirk, R. (2006). Statistics: An introduction. New York: Cengage Learning.

Ott, R., & Longnecker, M. (2008). An Introduction to Statistical Methods and Data Analysis. New York: Cengage Learning.

Weinberg, S., & Abramowitz, S. (2008). Statistics Using SPSS: An Integrative Approach. Cambridge: Cambridge University Press.

Appendices

SPSS Output Analyses

Case Processing Summarya
Cases
Included Excluded Total
N Percent N Percent N Percent
Race of Students 40 100.0% 0 0.0% 40 100.0%
Mathematics Scores for 12th Graders 40 100.0% 0 0.0% 40 100.0%
Science Scores for 12th Graders 40 100.0% 0 0.0% 40 100.0%
SAT Scores 40 100.0% 0 0.0% 40 100.0%
Gender of Students 40 100.0% 0 0.0% 40 100.0%
a. Limited to first 100 cases.
Case Summaries
Case Number Race of Students Mathematics Scores for 12th Graders Science Scores for 12th Graders SAT Scores Gender of Students
1 1 White American 72 86 700 Male
2 2 White American 62 85 725 Male
3 3 White American 75 75 680 Male
4 4 White American 80 74 659 Male
5 5 White American 95 62 692 Female
6 6 White American 83 78 726 Female
7 7 White American 69 75 653 Female
8 8 White American 82 84 625 Female
9 9 African American 78 79 702 Male
10 10 African American 82 63 560 Male
11 11 African American 56 56 640 Male
12 12 African American 64 68 580 Male
13 13 African American 65 65 520 Female
14 14 African American 52 64 623 Female
15 15 African American 49 69 536 Female
16 16 African American 75 76 573 Female
17 17 Hispanic 68 79 650 Male
18 18 Hispanic 71 81 653 Male
19 19 Hispanic 72 79 681 Male
20 20 Hispanic 73 76 702 Male
21 21 Hispanic 76 72 669 Female
22 22 Hispanic 75 75 632 Female
23 23 Hispanic 70 76 645 Female
24 24 Hispanic 78 74 663 Female
25 25 Latino 53 56 520 Male
26 26 Latino 48 62 450 Male
27 27 Latino 56 63 470 Male
28 28 Latino 52 56 380 Male
29 29 Latino 53 54 469 Female
30 30 Latino 54 58 473 Female
31 31 Latino 85 57 498 Female
32 32 Latino 46 56 502 Female
33 33 Asian 95 98 780 Male
34 34 Asian 88 95 720 Male
35 35 Asian 86 93 723 Male
36 36 Asian 84 93 760 Male
37 37 Asian 85 96 736 Female
38 38 Asian 87 98 690 Female
39 39 Asian 86 89 706 Female
40 40 Asian 89 92 715 Female
Total N 40 40 40 40 40

Frequencies

Statistics
Mathematics Scores for 12th Graders Science Scores for 12th Graders SAT Scores
N Valid 40 40 40
Missing 0 0 0

Frequency Table

Mathematics Scores for 12th Graders
Frequency Percent Valid Percent Cumulative Percent
Valid 46 1 2.5 2.5 2.5
48 1 2.5 2.5 5.0
49 1 2.5 2.5 7.5
52 2 5.0 5.0 12.5
53 2 5.0 5.0 17.5
54 1 2.5 2.5 20.0
56 2 5.0 5.0 25.0
62 1 2.5 2.5 27.5
64 1 2.5 2.5 30.0
65 1 2.5 2.5 32.5
68 1 2.5 2.5 35.0
69 1 2.5 2.5 37.5
70 1 2.5 2.5 40.0
71 1 2.5 2.5 42.5
72 2 5.0 5.0 47.5
73 1 2.5 2.5 50.0
75 3 7.5 7.5 57.5
76 1 2.5 2.5 60.0
78 2 5.0 5.0 65.0
80 1 2.5 2.5 67.5
82 2 5.0 5.0 72.5
83 1 2.5 2.5 75.0
84 1 2.5 2.5 77.5
85 2 5.0 5.0 82.5
86 2 5.0 5.0 87.5
87 1 2.5 2.5 90.0
88 1 2.5 2.5 92.5
89 1 2.5 2.5 95.0
95 2 5.0 5.0 100.0
Total 40 100.0 100.0
Science Scores for 12th Graders
Frequency Percent Valid Percent Cumulative Percent
Valid 54 1 2.5 2.5 2.5
56 4 10.0 10.0 12.5
57 1 2.5 2.5 15.0
58 1 2.5 2.5 17.5
62 2 5.0 5.0 22.5
63 2 5.0 5.0 27.5
64 1 2.5 2.5 30.0
65 1 2.5 2.5 32.5
68 1 2.5 2.5 35.0
69 1 2.5 2.5 37.5
72 1 2.5 2.5 40.0
74 2 5.0 5.0 45.0
75 3 7.5 7.5 52.5
76 3 7.5 7.5 60.0
78 1 2.5 2.5 62.5
79 3 7.5 7.5 70.0
81 1 2.5 2.5 72.5
84 1 2.5 2.5 75.0
85 1 2.5 2.5 77.5
86 1 2.5 2.5 80.0
89 1 2.5 2.5 82.5
92 1 2.5 2.5 85.0
93 2 5.0 5.0 90.0
95 1 2.5 2.5 92.5
96 1 2.5 2.5 95.0
98 2 5.0 5.0 100.0
Total 40 100.0 100.0
SAT Scores
Frequency Percent Valid Percent Cumulative Percent
Valid 380 1 2.5 2.5 2.5
450 1 2.5 2.5 5.0
469 1 2.5 2.5 7.5
470 1 2.5 2.5 10.0
473 1 2.5 2.5 12.5
498 1 2.5 2.5 15.0
502 1 2.5 2.5 17.5
520 2 5.0 5.0 22.5
536 1 2.5 2.5 25.0
560 1 2.5 2.5 27.5
573 1 2.5 2.5 30.0
580 1 2.5 2.5 32.5
623 1 2.5 2.5 35.0
625 1 2.5 2.5 37.5
632 1 2.5 2.5 40.0
640 1 2.5 2.5 42.5
645 1 2.5 2.5 45.0
650 1 2.5 2.5 47.5
653 2 5.0 5.0 52.5
659 1 2.5 2.5 55.0
663 1 2.5 2.5 57.5
669 1 2.5 2.5 60.0
680 1 2.5 2.5 62.5
681 1 2.5 2.5 65.0
690 1 2.5 2.5 67.5
692 1 2.5 2.5 70.0
700 1 2.5 2.5 72.5
702 2 5.0 5.0 77.5
706 1 2.5 2.5 80.0
715 1 2.5 2.5 82.5
720 1 2.5 2.5 85.0
723 1 2.5 2.5 87.5
725 1 2.5 2.5 90.0
726 1 2.5 2.5 92.5
736 1 2.5 2.5 95.0
760 1 2.5 2.5 97.5
780 1 2.5 2.5 100.0
Total 40 100.0 100.0

Histogram

Mathematics Scores for 12th Graders

Science Scores for 12th Graders

SAT Scores

One-way

ANOVA
Mathematics Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 38.025 1 38.025 .192 .664
Within Groups 7543.950 38 198.525
Total 7581.975 39
ANOVA
Science Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 55.225 1 55.225 .308 .582
Within Groups 6811.550 38 179.251
Total 6866.775 39

One-way

ANOVA
SAT Scores
Sum of Squares df Mean Square F Sig.
Between Groups 3783.025 1 3783.025 .382 .540
Within Groups 376177.950 38 9899.420
Total 379960.975 39

One-way

ANOVA
Sum of Squares df Mean Square F Sig.
SAT Scores Between Groups 3783.025 1 3783.025 .382 .540
Within Groups 376177.950 38 9899.420
Total 379960.975 39
Mathematics Scores for 12th Graders Between Groups 38.025 1 38.025 .192 .664
Within Groups 7543.950 38 198.525
Total 7581.975 39
Science Scores for 12th Graders Between Groups 55.225 1 55.225 .308 .582
Within Groups 6811.550 38 179.251
Total 6866.775 39

One-way

ANOVA
Mathematics Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 4603.850 4 1150.963 13.527 .000
Within Groups 2978.125 35 85.089
Total 7581.975 39

Post Hoc Tests

Multiple Comparisons
Dependent Variable: Mathematics Scores for 12th Graders
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 12.125* 4.612 .013 2.76 21.49
Hispanic 4.375 4.612 .349 -4.99 13.74
Latino 21.375* 4.612 .000 12.01 30.74
Asian -10.250* 4.612 .033 -19.61 -.89
African American White American -12.125* 4.612 .013 -21.49 -2.76
Hispanic -7.750 4.612 .102 -17.11 1.61
Latino 9.250 4.612 .053 -.11 18.61
Asian -22.375* 4.612 .000 -31.74 -13.01
Hispanic White American -4.375 4.612 .349 -13.74 4.99
African American 7.750 4.612 .102 -1.61 17.11
Latino 17.000* 4.612 .001 7.64 26.36
Asian -14.625* 4.612 .003 -23.99 -5.26
Latino White American -21.375* 4.612 .000 -30.74 -12.01
African American -9.250 4.612 .053 -18.61 .11
Hispanic -17.000* 4.612 .001 -26.36 -7.64
Asian -31.625* 4.612 .000 -40.99 -22.26
Asian White American 10.250* 4.612 .033 .89 19.61
African American 22.375* 4.612 .000 13.01 31.74
Hispanic 14.625* 4.612 .003 5.26 23.99
Latino 31.625* 4.612 .000 22.26 40.99
*. The mean difference is significant at the 0.05 level.

One-way

ANOVA
Science Scores for 12th Graders
Sum of Squares df Mean Square F Sig.
Between Groups 5853.900 4 1463.475 50.571 .000
Within Groups 1012.875 35 28.939
Total 6866.775 39

Post Hoc Tests

Multiple Comparisons
Dependent Variable: Science Scores for 12th Graders
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 9.875* 2.690 .001 4.41 15.34
Hispanic .875 2.690 .747 -4.59 6.34
Latino 19.625* 2.690 .000 14.16 25.09
Asian -16.875* 2.690 .000 -22.34 -11.41
African American White American -9.875* 2.690 .001 -15.34 -4.41
Hispanic -9.000* 2.690 .002 -14.46 -3.54
Latino 9.750* 2.690 .001 4.29 15.21
Asian -26.750* 2.690 .000 -32.21 -21.29
Hispanic White American -.875 2.690 .747 -6.34 4.59
African American 9.000* 2.690 .002 3.54 14.46
Latino 18.750* 2.690 .000 13.29 24.21
Asian -17.750* 2.690 .000 -23.21 -12.29
Latino White American -19.625* 2.690 .000 -25.09 -14.16
African American -9.750* 2.690 .001 -15.21 -4.29
Hispanic -18.750* 2.690 .000 -24.21 -13.29
Asian -36.500* 2.690 .000 -41.96 -31.04
Asian White American 16.875* 2.690 .000 11.41 22.34
African American 26.750* 2.690 .000 21.29 32.21
Hispanic 17.750* 2.690 .000 12.29 23.21
Latino 36.500* 2.690 .000 31.04 41.96
*. The mean difference is significant at the 0.05 level.

One-way

ANOVA
SAT Scores
Sum of Squares df Mean Square F Sig.
Between Groups 323701.600 4 80925.400 50.345 .000
Within Groups 56259.375 35 1607.411
Total 379960.975 39

Post Hoc Tests

Multiple Comparisons
Dependent Variable: SAT Scores
LSD
(I) Race of Students (J) Race of Students Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
White American African American 90.750* 20.046 .000 50.05 131.45
Hispanic 20.625 20.046 .311 -20.07 61.32
Latino 212.250* 20.046 .000 171.55 252.95
Asian -46.250* 20.046 .027 -86.95 -5.55
African American White American -90.750* 20.046 .000 -131.45 -50.05
Hispanic -70.125* 20.046 .001 -110.82 -29.43
Latino 121.500* 20.046 .000 80.80 162.20
Asian -137.000* 20.046 .000 -177.70 -96.30
Hispanic White American -20.625 20.046 .311 -61.32 20.07
African American 70.125* 20.046 .001 29.43 110.82
Latino 191.625* 20.046 .000 150.93 232.32
Asian -66.875* 20.046 .002 -107.57 -26.18
Latino White American -212.250* 20.046 .000 -252.95 -171.55
African American -121.500* 20.046 .000 -162.20 -80.80
Hispanic -191.625* 20.046 .000 -232.32 -150.93
Asian -258.500* 20.046 .000 -299.20 -217.80
Asian White American 46.250* 20.046 .027 5.55 86.95
African American 137.000* 20.046 .000 96.30 177.70
Hispanic 66.875* 20.046 .002 26.18 107.57
Latino 258.500* 20.046 .000 217.80 299.20
*. The mean difference is significant at the 0.05 level.

One-way

ANOVA
Sum of Squares df Mean Square F Sig.
Mathematics Scores for 12th Graders Between Groups 4603.850 4 1150.963 13.527 .000
Within Groups 2978.125 35 85.089
Total 7581.975 39
Science Scores for 12th Graders Between Groups 5853.900 4 1463.475 50.571 .000
Within Groups 1012.875 35 28.939
Total 6866.775 39
SAT Scores Between Groups 323701.600 4 80925.400 50.345 .000
Within Groups 56259.375 35 1607.411
Total 379960.975 39

Correlations

Correlations
Mathematics Scores for 12th Graders SAT Scores
Mathematics Scores for 12th Graders Pearson Correlation 1 .726
Sig. (2-tailed) .000
N 40 40
SAT Scores Pearson Correlation .726 1
Sig. (2-tailed) .000
N 40 40