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# Assignment Example

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My conclusion is that there is a difference in math scaled scores between different ethnic groups, as can be seen by the very large difference between the sum of squares between ethnic groups and within them.
b. My conclusions are that there is a difference due to the…

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1. A. Paired-sample t-test between “math scaled score” and “Terra Nova 4th grade math score” a. The null hypothesis is that there is no difference between the maths scaled score and the Terra Nova 4th grade math score.
b. My conclusion is that there is definitely a difference between both grades. The null hypothesis is rejected!
B. ANOVA comparing math scaled score among different ethnic groups
a. The null hypothesis is that the averages in the math tests among ethnic groups are similar (or the same).
b. The independent variable is the ethnic group characteristic, and the dependent variable is the math scaled score.
c. My conclusion is that there is a difference in math scaled scores between different ethnic groups, as can be seen by the very large difference between the sum of squares between ethnic groups and within them.
C. Multiple regression with “math scaled score” as dependent variable and “gender”, “ELA scaled score”, and “Terra Nova 4th grade math score” as independent variables.
a. The null hypotheses are that the independent variables dont affect the dependent one (math scaled score) and that it is the same regardless of these independent variables.
b. My conclusions are that there is a difference due to the independent variables, as it is seen that even after calculating the regression, the residual aspect is still strong enough to make a difference, suggesting that the independent variables do affect the outcome of the math scaled test.
c. The independent variable that is the best predictor of the math scaled score is the ELA scaled score. Its standard error is small and so is his beta value.
2. A random sampling means not choosing and selecting people for the tests, making the test subjects random. This means that the test subjects wont necessarily be representative of the population. Random assignment means assigning test subjects to different treatments in the study. Randomization is the best way of making sure that the necessary control in the study is present. They are related to both internal and external validities as they increase both. Internal validity is the validity of the effect discovered in the study, and external validity is the validity in which the cause-effect relationship holds up when measurements are changed. The randomization increases both validities.
3.
a. Threats to the validity of the research about the two school groups include the fact that the number of students in each group isnt specified, and if it isnt above 30- the research isnt valid since at least 30 test subjects are needed to conduct a test on statistical hypotheses (even more according to different, more rigid approaches).
A way to increase the external validity in this subject is to increase the number of test subjects in each group as much as possible, so that the results are as accurate and representative as possible, and also in order for them to be at least over 30, which is the agreed upon number of test subjects needed in a group in order to be able to test the validity of hypotheses.
b. The threat to the validity of the study is mainly that the teacher had a pretest and a posttest for classes A and B while only having the posttest for classes C and D. it is impossible to deduce from this that the former classes are superior to the latter ones because of the introduction of the new materials and methods. She should have done both tests on all classes. Furthermore, there is a need to control possible intervening variables to make sure that there is a statistical link between these new materials and methods to the score achieved in the post test (the link can be a correlation and then it wouldnt be legitimate to make this assumption about the results).
In order to increase the external validity, one must consider the Aptitude-Treatment-Interaction. There is a need to make sure that there are no intervening variables, and in this case- there may certainly be ones. Therefore, the researcher should control all relevant variables in order to exclude them as possible intervening ones in the results of the study. Also, the teacher needed to make sure to do both pretest and posttest for all classes because it is impossible to evaluate progress when only giving certain classes the posttest while giving others both tests. As for internal validity, the teacher sounds a bit biased. This bias needs to be removed in order for the study to be appropriate. She needs to remove the feature of selection bias and treat all the children exactly the same, giving them all the same tests rather than doing what shes done.
4. In order to design an ideal experiment that will check if children
who watch harmonious interactions with other people from other racial background will show a more positive approach to these people than will children who watch racial conflicts, many things need to be done. I will plan the research so that the study would follow these children starting from a young age in which they dont view these movies yet to establish a baseline for their approach to people from other racial background. The study will follow them for at least 15 years to see the changes in their approaches toward these people. Certain things will be carefully scrutinize like the collection of data and the use of proper statistical tools and methods. Ill make sure Ill have as many test subject as possible (with a minimum of 30 per each group to match the requirement for a hypothesis testing) and use randomization (random sampling as well as random assigning) to make sure the internal and external validities are maximized. Finally, the results will be analyzed very carefully to make sure that no mistakes are present. This will yield the ideal experiment for this subject. Read More
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