Statistics Final Exam Study Guide

Essay 1 

In this experiment, the researchers sought to identify the more effective method of flu prevention. Therefore, the research question was to determine which flu prevention method is more effective. As a result, the hypothesis states that the nasal spray is more effective as a flu vaccine compared to the flu shot in a randomly selected population. The alternative hypothesis would be that the flu shot is a more effective flu vaccine within the same conditions.

To determine whether the test was statistically significant, the p-value is observed against the level of significance. At first instance, one notes that the p-value is significantly lower than the significance level set (0.008 compared to 0.05). Therefore, it can be assumed that the null hypothesis is false and the alternative hypothesis holds true for the compared results of the nasal spray and flu shot. In this case, the researchers would then reject the null hypothesis.

Considering the outcomes of both values in their proportions, similar t-score and p-values, the alternative hypothesis has sufficient evidence to support it. This is because the individual data shows a proportion of infection after the nasal spray compared to flu shots, thereby offering a comparative approach to the results for both outcomes. Nevertheless, one of the challenges of random sampling is the possibility of generalization. While the study population shows strong responses to flu shots, this does not provide the accurate picture on the ground due to generalization. Simple random sampling does not give sufficient ground to analyze different demographic factors that might affect the application of the study.

Nevertheless, a follow-up study with systematic sampling can be done to obtain a demographic-sensitive study accommodating different factors including race, income and education levels. This way, the study can become practically significant, in that it can be applied to a real-life situation, compared to its statistical significance, which means it can only be applied in an ideal environment.

Essay 2 

Correlation is a statistical test that finds the direction of the linear relationship between two phenomena subjected to statistical testing. In this case, the value .75 shows that the two variables have a strong positive linear relationship. This then means that a strong linear relationship is present between in the IQ of an individual with their GPA. Nevertheless, these results indicate that the researchers assumed that the relationship between IQ and GPA is purely linear, thereby eliminating chances that the relationship could be curved. As a result, correlation testing is limited as it can only measure linear relationships between phenomena. Additionally, only two items can be measured at a time.

Having said this, this correlation is strong, and in the positive direction. This means that high IQ individuals are more likely to have higher GPA. Nevertheless, evidence is not provided as to whether increasing IQ leads to increased GPA. This is because other factors such as school attendance and additional study among others may influence individual GPA units aside from their IQ. Correlation and causation are different, in that causation results in the tangible effect on the second variable, while correlation only predicts the relationship between two variables. That said, correlation is not a good measure for GPA, noting that GPA depends on multiple variables for proper expression and is not just a function of the variable, IQ.

Essay 3 

Consider the datasets, which have been arranged in ascending order and divided in two groups of ten. The descriptive statistics as calculated on MS Excel are as follows:

Dataset 1a			Dataset 1b
Mean	3.48		Mean	9.24
Standard Error	0.29769		Standard Error	0.70745
Median	3.3		Median	8.85
Mode	#N/A		Mode	9.5
Standard Deviation	0.94139		Standard Deviation	2.23716
Sample Variance	0.88622		Sample Variance	5.00489
Kurtosis	-1.5709		Kurtosis	6.86883
Skewness	0.19022		Skewness	2.44392
Range	2.6		Range	7.9
Minimum	2.2		Minimum	7.3
Maximum	4.8		Maximum	15.2
Sum	34.8		Sum	92.4
Count	10		Count	10

Data set 1a and 1b refers to the first ten values and second ten values respectively as separated above. The two groups differ in that the variance among the smaller reaction times is greater than that of the second group. Moreover, there exists a greater range between the sample values. Outliers exist in the groups and make the mean significantly change. This explains the higher mean for the second group compared to the first group. This effect is clarified after the second test. When the values are doubled so that there are 20 values in each segment, the following is obtained:

Dataset 2a			Dataset 2b
Mean	3.48		Mean	9.24
Standard Error	0.20489		Standard Error	0.4869
Median	3.3		Median	8.85
Mode	2.2		Mode	9.5
Standard Deviation	0.91629		Standard Deviation	2.17749
Sample Variance	0.83958		Sample Variance	4.74147
Kurtosis	-1.4973		Kurtosis	4.72757
Skewness	0.17372		Skewness	2.2319
Range	2.6		Range	7.9
Minimum	2.2		Minimum	7.3
Maximum	4.8		Maximum	15.2
Sum	69.6		Sum	184.8
Count	20		Count	20

Increase in sample size does not increase mean, however. Nevertheless, the effect is felt on the median and mode. Due to the small change in sums and count, the change is equally experienced in the standard deviation and variance.

Part 2: Article Critique 

This section chose to review an article investigating factors that were in play for the successful employment of transition-age youth with visual impairment challenges. Little research was done on the factors that affected successful transition from school to employment for youth with visual impairment (McDonnall & Crudden, 2009). The purpose of the study with its qualification was not adequately stated within the study. As a result, it was necessary to extrapolate, from the introductory section, that the lack of employment among youth with visual disability was the main reason behind the study. The statistics used, however, could form the basis for a statement of the purpose of the study.

In the literature review, a discussion of the variables in play for visually impaired youth employment was discussed. Different variables such as work experience, self-esteem, academic competence, assistive technology and the locus of control were discussed as key factors influencing employment of visually impaired persons (McDonnall & Crudden, 2009). Previous studies were used to show correlation between individual variables and employment. Notably, however, specific research on persons with visual impairments was not used. Instead, different parameters including persons in high school, disabled persons, and university graduates were tackled. Furthermore, the definition of employment was not clearly stated to include full-time, part-time or temporary forms of employment.

Concerning the methodology, the hypotheses were as follows (McDonnall & Crudden, 2009, p. 331):

Early work experiences will be associated with employment.

Academic competence will be associated with employment.

Self-determination skills will be associated with employment.

Higher levels of self-esteem will be associated with employment.

The research questions were as follows (McDonnall & Crudden, 2009, p. 331):

Is the use of assistive technology or devices associated with employment?

Is involvement with the counselor in the vocational rehabilitation process associated with employment?

Is an internal locus of control associated with employment?

Therefore, it was extrapolated that the independent variable was employment while dependent variables were the individual’s work experience, self-esteem, academic competence, individual use of technology, locus of control and access and involvement to a counselor. Each measure was explained in detail with specifics and limitations on their measurement. Nevertheless, intervening variables were not identified. Nevertheless, other studies have identified such variables including access to print material and job shadowing. Additionally, social networks work as confounding variables as youth with large networks are more likely to gain access to employment.

The study population was taken from Cornell’s Website LSVRSP through the use of a multistate complex design. The final sample contained 41 respondents – a rather small sample with a database containing over eight thousand individuals. However, the explanation was provided. It could be assumed that majority of individuals in this category, with visual impairments were above 21 years, which was the age limit. Uni-variate measures of analysis were used due to the small sample size, including logistic regress and t-tests.

Based on the study design, the intention of the researchers could have been to use a correlational study design. Inferential and descriptive statistics were largely used in this data analysis, in which ANOVA testing and t-tests were used. Significance level was set at .10 to enable the practical significance of the study results. After calculating, it was found that work experience, involvement with a counselor and self-esteem were not statistically significant for the establishment of the relationship. Nevertheless, other factors reached statistical significance (McDonnall & Crudden, 2009).

For the discussion, therefore, focus was on the remaining factors that had reached significance, relating them to previous research. Although surprising facts were not found by this study, it is a point to note that work experience, locus of control and self-determination are important considerations as they influence access to employment. Therefore, the article contributes to knowledge as it establishes the relationship between employment and an array of factors including assistive technology, academic competence, self-determination, work experience and locus of control. As a result, counselors can find this information useful for rehabilitation programs involving persons with visual impairments.

References

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.

McDonnall, M. C., & Crudden, A. (2009). Factors affecting the successful employment of transition-age youths with visual impairments. Journal of Visual Impairment & Blindness, 103(6) , 329.