Step 1. Read the scenario and then choose a test from the list here for data ana

Question

Step 1. Read the scenario and then choose a test from the list here for data analysis: (1 point)

Correlation

Single-sample t test

Dependent-means (dependent-samples) t test

Independent-means (independent-samples) t test

Analysis of variance

Chi-square for goodness of fit

Chi-square for independence

Step 2. Justify your chosen test by identifying the variable(s) in the scenario (1 point) and the type of each variable (e.g. categorical, ordinal, continuous… etc.) (1 point) that prompted you to select the test. Relate the variable(s) to your choice clearly (.5 point)

Example:

I wonder if PE class in school is related to student’s overall physical activities after school. Specifically, the research question is: Does the after-school physical activity level differ among students from a school that doesn’t offer PE class, students from a school that offers PE as an elective, and students from a school that offers PE as a requirement.

Chosen test: Analysis of Variance

Rationale: The dependent variable is continuous so a parametric test can be performed. The independent variable is PE class type with three categories so ANOVA is chosen to compare the three groups.

A) A recent poll with a sample of 1000 voters show that presidential candidate A has the support of 543 of the voters while candidate B has the support of 457 voters. Research question: Do people prefer candidate A or are people evenly split in their support?

Chosen test:

Rationale:

B) A middle school is assessing the potential benefit of implementing e-readers with a large collection of electronic books in the English classroom as a replacement for the usual collection of printed books. They designate one class as the e-book group and another class as the printed book group and then assess their performance on a test of reading comprehension after a whole semester. Research question: Does the e-book group perform differently from the printed-book group?

Chosen test:

Rationale:

C) A social psychologist wonders if using social media is related to the user’s satisfaction with his/her life. He collects data from a large sample of young adults on the amount of time they spend on social media and on the satisfaction level they feel toward their own lives at present. Research question: Is there a relationship between social media usage level and life satisfaction level?

Chosen test:

Rationale:

D) A research team is interested in the long-term effect of psychotherapy for depression after the patients have completed a three-month treatment plan. They administered a comprehensive depression scale to the patients upon completion of the psychotherapy treatment and then follow up with them 6 months later with the same comprehensive depression scale. Research question: Do the patients have significantly more depressive symptoms 6 months after the treatment compared to their condition right after the treatment period?

Chosen test:

Rationale:

Explanation / Answer

A) A recent poll with a sample of 1000 voters show that presidential candidate A has the support of 543 of the voters while candidate B has the support of 457 voters. Research question: Do people prefer candidate A or are people evenly split in their support?

Chosen test: Single Sample t – test for Proportions.

Rationale: Here we shall consider sampling from a population which is divided into two mutually exclusive and collectively exhaustive classes – one class possessing a particular attribute, Say A and other class not possessing that attribute, and then note down the number of persons in the sample of size n, possessing that attribute. The presence of an attribute in sampled unit may be termed as success and its absence as failure. In this case a sample of n observations is identified with that of a series of n independent Bernoulli trials with constant probability P of success for each trial.

B) A middle school is assessing the potential benefit of implementing e-readers with a large collection of electronic books in the English classroom as a replacement for the usual collection of printed books. They designate one class as the e-book group and another class as the printed book group and then assess their performance on a test of reading comprehension after a whole semester. Research question: Does the e-book group perform differently from the printed-book group?

Chosen test: Chi-square for independence

Rationale: Let us consider two attributes, A and B, A divided into 2 classes A1 and A2 (two parts of class) and B divided into 2 classes (two set of readers viz. e-book readers and usual readers of printed books). Such a classification in which attributes are divided into two or more classes is known as manifold classification. The various cell frequencies can be expressed in 2 x 2 manifold contingency table and check if there is any association between type of reading (e-book and printed book) over performances in reading comprehension after a semester. The problem is to test if the two attributes A and B under consideration are independent or not. The exact test for the independence of attributes is very complicated but a fair degree of approximation is given, for large samples by chisquare good ness of fit.

C) A social psychologist wonders if using social media is related to the user’s satisfaction with his/her life. He collects data from a large sample of young adults on the amount of time they spend on social media and on the satisfaction level they feel toward their own lives at present. Research question: Is there a relationship between social media usage level and life satisfaction level?

Chosen test: Correlation

Rationale: This is bivariate distribution. One variable is amount of time spent on social media and another variable is satisfaction level (may be on a scale of 1 to 10, just an example). We are interested to findout if there is any correlation or covariance between the two variables under study. If the change in one variable affects a change in the other variable, the variables are said to be correlated. If the two variables deviate in the same direction, i.e., if the increase (of decrease) in one results in a corresponding increase (or decrease) in the other, correlation is said to be direct or positive. But if they constantly deviate in the opposite directions, then correlation is said to be diverse or negative. Correlation is said to be perfect if the deviation in one variable is followed by a corresponding and proportional deviation in the other. Therefore, for the above research, correlation is best to use to find relationship between social media usage and life satisfaction.

D) A research team is interested in the long-term effect of psychotherapy for depression after the patients have completed a three-month treatment plan. They administered a comprehensive depression scale to the patients upon completion of the psychotherapy treatment and then follow up with them 6 months later with the same comprehensive depression scale. Research question: Do the patients have significantly more depressive symptoms 6 months after the treatment compared to their condition right after the treatment period?

Chosen test: Independent-means (independent-samples) t test (t test for difference of means)

Rationale: Here, we want to test two dependent samples of treatment. One before treatment and second, after treatment, and depression scale points are noted. Compute the mean of points and compare if there is any significant difference between average of points before treatment and after treatment, and check if there is any significant decrease after treatment under the assumption that both variances are equal or significantly equal.

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