Psychology

Section I
The data is obtained from 9th grade students performance and behavior data. The data consists of 216 observations that will be used for the analysis. The variables of interest for the analysis are the Social Adjustment Problems of 9th grade students and the 9th Grade students that dropped out of High School. Both variables are of nominal level of measurement.

Section II
Pearson chi-square test will be used to determine whether there is a relationship between social adjustment problems of 9th grade students and the number of 9th grade students who dropped out of high school. In order to use Chi-square test, certain assumptions should be verified first. The following are the assumptions of Chi-square test random sample data, sufficiently large sample size and adequate cell sizes (Howell, 2008). In order to verify the assumptions, crosstabulation of the data will be used. In addition, bar graph will also be used to verify the assumptions.

First assumption to be tested is the random sampling. Random samples obtained in the observation depend on how the data are obtained from the participants of the 9th grade students performance and behavior data. As far as the survey data is concerned, researchers always try to obtain the data as random as possible. In case, the data is not randomly sampled, the analysis is still conducted for the sake of discussion.

The second assumption to be tested is the sufficiency of the number of samples for Pearson Chi-square test. In using Pearson Chi-square test, there should be at least 20 samples for the test. The number of samples that will be used for the test is equal to 216 observations. Since the number of observations is greater than the minimum sample requirement, then the assumption is verified.

The last assumption to be tested is the adequate cell sizes. In Pearson Chi-square test, it is required that each cell must have a size of at least 5. In order to check whether the data satisfies the assumption, crosstabulation will be used.

Table 1
Crosstabulation of Social Adjustment Problems and Dropped out of High School
Social Adjustment Problems in 9th Grade  Dropped out of High School CrosstabulationDropped out of High SchoolTotalNoYesSocial Adjustment Problems in 9th GradeNoCount18110191Expected Count173.317.7191.0 within Social Adjustment Problems in 9th Grade94.85.2100.0 within Dropped out of High School92.350.088.4 of Total83.84.688.4YesCount151025Expected Count22.72.325.0 within Social Adjustment Problems in 9th Grade60.040.0100.0 within Dropped out of High School7.750.011.6 of Total6.94.611.6TotalCount19620216Expected Count196.020.0216.0 within Social Adjustment Problems in 9th Grade90.79.3100.0 within Dropped out of High School100.0100.0100.0 of Total90.79.3100.0 Table 1 shows the crosstabulation of the social adjustment problems and dropped out of high school in 9th grade students. From the table, one can see that the frequency of students who has no Social adjustment problem and does not dropped out of high school is larger than the other categories with a count of 181. The value accounts for 83.8 of the total observations. On the other hand,  students who have Social adjustment problem and does not dropped out of high school has an observed frequency of 15 which accounts for 6.9 of the total observation.  Students who have no Social adjustment problem and dropped out of high school has an observed frequency 10 which accounts for 4.6 of the total observation. While, students who have Social adjustment problem and does dropped out of high school has an observed frequency 10 which accounts for 4.6 of the total observation. One can see that all of the cell have a size of greater than 5 except for the cell of 9th grade students with Social Adjustment problems and have dropped out of high school with only 2.3 cell size on expected count. Thus, the assumption of adequate cell sizes is violated.

Figure 1. Bar Chart of Social Adjustment Problems in 9th Grade Students.
From the figure, one can see that the frequency of students who has no Social adjustment problem and does not dropped out of high school is larger than the other categories. It is followed by 9th grade students with social adjustment problems and does not dropped out of high school. Both students that dropped of high school even with or without social adjustment problems have the same level of count.

After verifying the assumptions of the test, it has been found out that the data violated one of the important assumptions, adequate cell sizes. In order to correct the assumption, Yates correction will be applied for the Pearson-Chi square test statistic. Otherwise, the Pearson Chi-Square test will still be conducted for the sake of discussion.

Section III
In order to use Pearson Chi-square test, the researcher must set the alpha level on which the test will be conducted. The alpha level to be used for the test is 0.05 significance level. The following are the research question and the hypotheses for the test.

Research Question
Is there a relationship between Social Adjustment Problem and dropping out of 9th grade students

Research Hypothesis
There is a relationship between social Adjustment Problem and dropping out of 9th grade students.

Null hypothesis
There is no relationship between social Adjustment Problem and dropping out of 9th grade students.

The decision is to reject the null hypothesis when the p-value of the chi-square statistic is less than 0.05. Otherwise, the researcher will fail to reject the null hypothesis.

Section IV
After conducting Pearson Chi-square test, the following results were obtained.
Table 2
Chi-Square Test
Chi-Square TestsValuedfAsymp. Sig. (2-sided)Exact Sig. (2-sided)Exact Sig. (1-sided)Pearson Chi-Square31.799a1.000Continuity Correctionb27.7961.000Likelihood Ratio21.1591.000Fishers Exact Test.000.000Linear-by-Linear Association31.6521.000N of Valid Cases216a. 1 cells (25.0) have expected count less than 5. The minimum expected count is 2.31.b. Computed only for a 2x2 table
From the table, one can see that the Pearson Chi-square statistic is equal to 31.799. The corresponding p-value of the test statistic is less than 0.001. Since the p-value of the Pearson Chi-square Statistic is less than 0.05 significance level, the researcher rejects the null hypothesis. In addition, the continuity correction statistic is equal to 27.796 with a corresponding p-value of less than 0.001. Since the p-value of the continuity correction (Yates Correction) is less than the significance level of 0.05, and then the researcher is still able to reject the null hypothesis. Thus, the researcher is 95 confident that there is a relationship between social Adjustment Problem and dropping out of 9th grade students.

However, Pearson Chi-square test only determines the relationship between the two variables. The Pearson Chi-square Statistic is not able to test for the strength of the association between the two variables. In order to determine the strength of relationship between the variables, the researcher will used Phi and Cramer V statistic (Garson, 2008). After conducting Phi and Cramer V test, the following results were obtained.

Table 3
Symmetric Measures
Symmetric MeasuresValueApprox. Sig.Nominal by NominalPhi.384.000Cramers V.384.000N of Valid Cases216

From the table, one can see that the value of Phi and Cramers V statistic are both equal to 0.384. Both have the same p-value which is less than 0.001. Phi and Cramers V are interpreted like correlation coefficient. Thus, the value denotes that there is an increasing relationship between social adjustment problem and dropping out of 9th grade students. In addition, the p-value of symmetric measures is less than 0.05 significance level.  Thus, the null hypothesis that there is no significant relationship between social adjustment problem and dropping out of 9th grade students is rejected. Therefore, the researcher is 95 confident that there is a significant relationship between social adjustment problem and dropping out of 9th grade students.