Quantitative Research Methods solution

What to do to encourage young people to do STEM topics

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What to do to encourage young people to do STEM topics

Before the analysis, a thorough check important to validate the quality of the dataset. Faulty entries can reconfirm or removed in cases where the original values cannot be found. In this dataset, entries for one of the female participants’ record had inflated entries for the first, second and third recording. Therefore, this individual was not included in the analysis. Exclusion on this entry reduces the bias of statistical conclusion drawn from results obtained from the data. Using these extreme values can inflate the differences being observed, hence leading to wrong inferences.

Table 1: A table showing summary statistics for the attitude scores for the time points

1. Do attitudes to STEM improve over time?

The measurements of attitudes are continuous measures of central tendency are the appropriate statistics to evaluate the overall trend of the scores. An analysis for the summary statistics will be conducted and used to compare the statistics among the timepoints. In this case, mean or median plots can be opted, which can provide a visual solution, hence supporting the decision on whether there was an overall increase. Also, other plots such as boxplots can be used to compare the distributions. Further, individual line plots can be used to observe the overall change in the score from the baseline to the third recording.

Table 2: Analysis of the attitude scores for the four timepoints

On average, we can see that there was an increase from 24.26 to 26.55. all the scores were skewed to the right, indicating that there were participants whose scores were generally high, hence introducing right skewness in the data.

Figure 1: Mean and boxplots for the four-time points

In the above plots, we can slightly observe an increase in means of the score. There is a slightly steep increase between the average scores obtained from event 2 and event 3. Observing the boxplots, which shows the distribution of the score, we can observe that there is no much difference in the distributions among the four-time points. Further, after observing an increase from baseline to event 3, one-way ANOVA is appropriate to test whether the difference in means is significant (Olive, 2017; Ross & Willson, 2017).

Table 3: One-way ANOVA model

After performing the one-way ANOVA, the findings show that neither of the means is statistically different from the others at 95% confidence level. Therefore, we conclude that an increase in attitude scores towards taking a STEM topic.

 Having a parent who has completed higher education has been recorded as a categorical variable, and the level of engagement was recorded as a continuous variable, with higher values showing higher engagement levels. Therefore,  the best method to check whether having a parent who had completed higher education level had any influence on the engagement would be to check whether the means are statistically different between the two groups. To achieve this, we will perform a one sample t-test. Before the statistical test, we can also use boxplots to visualize the distribution of the engagement scores in the two groups.

Figure 2: Boxplot for engagement scores by whether a parent had high education or not

According to the plot above, students whose parents completed higher education have lower engagement scores score to their counterparts. In both groups, there are extreme values, hence right-skewed distributions. Therefore, the Mann-Whitney U test (non-parametric method) is the most appropriate method to test for the difference in median values.

Table 4: Median ranks

Table 5: Test statistics

The test has a p-value less than a significance level of 5%. Therefore, we conclude that there is a statistically significant difference in median values of engagement score between students whose parents had higher education compared to their counterparts.

In this case, we have two categorical variables and one continuous variable. The analysis will focus on checking whether SES quantile influence on engagement is affected gender. A two-way ANOVA model is the ideal statistical approach to answer this question effectively. Visual plots, such as boxplot or mean plots can be used to investigate the distribution on the engagement score about the two categorical variables.

Figure 3: Boxplots of engagement scores by SES quantile and gender

As seen in the plot above, there is variability in engagement score between males and females in each social status class. Further, we will use a two-way ANOVA model to check whether the variation is statistically significant (Elliott & Woodward, 2007).

Table 6: Two-way ANOVA model

The interaction between gender and social, economic status is not statistically significant at a 5% significance level. We conclude that engagement levels among social, economic classes are not dependent on the gender of a student. Therefore, controlling for the different social, economic status, it does not matter whether the student is male or female in regards to their engagement scores.

The self-reported satisfaction levels are continuous values; hence one sample t-test is the appropriate method to check whether there is a significant difference between the groups. Further, based on whether the self-reported satisfaction level score is normally distributed or not, a parametric or non-parametric method is adopted.

Table 7: Normality test

The normality test method has a null hypothesis that assumes that the data is normally distributed. Based on the normality tests above, the satisfaction level is not normally distributed. Therefore, we opt using the non-parametric method – Mann-Whitney U test of equality of median values (Ghasemi & Zahediasl, 2012).

Table 8: Median values of satisfaction score for those liking languages and maths

Table 9: Test statistics

Comparing the mean ranks, students liking mathematics have higher mean ranks compared to those liking languages. Following the test statistics, we conclude that there is a significant difference in self-reported satisfaction scores between student liking mathematics and those liking languages.

References

Elliott, A. C., & Woodward, W. a. (2007). Analysis of Categorical Data. Statistical Analysis Quick Reference Guidebook, 113–150. https://doi.org/10.1007/SpringerReference_60770

Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486–489. https://doi.org/10.5812/ijem.3505

Olive, D. J. (2017). One Way ANOVA. In Linear Regression (pp. 175–211). https://doi.org/10.1007/978-3-319-55252-1_5

Ross, A., & Willson, V. L. (2017). One-Way ANOVA. Basic and Advanced Statistical Tests, 21–24. https://doi.org/https://doi.org/10.1007/978-94-6351-086-8_5