using the t test in an experimental research design

Question 1 If Mary wants to study the impact of background noise level on sixth grader learning in a math lesson, the independent variable is the background noise condition. Mary has decided to use a t-test, which means that she will only have two conditions that differ from one another (“T Test (Student’s T-Test),” n.d.). In this case, the experimental condition would be high background noise (measured by decibel level perhaps), and the control condition would be low background noise (also measured by decibel level).

The independent variable in this experiment would be learning in a mathematics lesson. Learning can be assessed using a number of different instruments appropriate to the specific lesson, with a simple quantifiable quiz the most appropriate. A quiz that had absolute right or wrong answers, whether by solving a math problem or answering multiple choice questions, would help to standardize the results and minimize bias. Mary would have to choose a lesson that was age-appropriate, and administer exactly the same lesson to all students.

Likewise, all students would have to take exactly the same math assessment. The results of the math assessment for each group would be the dependent variable. Each participant would have one score: either by averaging all the answers in a multi-item quiz or by computing the answer of one math problem. Internal validity would be stronger in a multi-item quiz.

A continuous scale of measurement could be used, but is not necessary in this case because there is no need to divide the numerical data into infinitely small incremental units (“Scales of Measurement,” n.d.). Mary will be working with ordinal scales of measurement if she uses a math quiz with multiple-choice questions. However, Mary could choose to use a continuous scale of measurement when computing the average score for each student’s test. References “Scales of Measurement,” (n.d.).

https://stattrek.com/statistics/measurement-scales.aspx “T Test (Student’s T-Test): Definition and Examples,” (n.d.). Statistics How To. http://www.statisticshowto.com/probability-and-statistics/t-test/ Question 2 The null hypothesis in Mary’s study is that noise level has no bearing on student learning in a sixth grade math class. That is, students who are exposed to the condition of hearing continuous and loud background noise performed the same on the math test as students assigned to the no-noise condition.

The alternative hypothesis for Mary’s study would be that noise levels have an adverse impact on student learning, with the experimental group scoring lower on the test than their counterparts in the no-noise condition. Now that Mary has collected her data, she needs to confront underlying assumptions before correctly applying the t-test and testing the hypotheses. One thing Mary should do is calibrate student scores from both groups.

Because Mary needs to use two different groups of students, randomly assigned to each condition, she assumes that all the students will have roughly equal distribution of scores. It is actually possible that by coincidence, one group contains high performing students in greater proportion to the other group. To control for this, Mary could administer a pretest to assess prior knowledge and compare the posttest scores with those on the pretest.

This way, Mary would be assessing learning based on the baseline of prior knowledge rather than on the assumption that all students were starting from the same place. Mary does not have.