Question

A psychologist studying the effects of positive thinking" on cognitive ability designs the following study: 120 male volunteers are divided into two groups by random assignment. Eighty female volunteers are randomly divided into two groups of 40 by the same method. One group of 60 males and 40 females is asked to write down three things they feel that they are good at doing. The other group of 60 males and 40 females is asked to write down what they ate for breakfast. All 100 subjects then take a SAT Math practice test, and the means for the two groups are compared. Which of the following is a correct description of this study?

i. An observational study

ii. A completely randomized experiment

iii. A matched pairs experiment

iv. A stratified random experiment

v. A randomized block experiment

Answer 1

This study is a stratified random experiment, employing random assignment within gender strata to compare the effects of positive thinking on cognitive ability, ensuring a more controlled and meaningful analysis.

Step-by-step explanation:

This study is a stratified random experiment because the participants are first divided into strata based on gender, and then within each stratum, random assignment is used to form the two groups—one focused on positive thinking and the other on a neutral task (writing about breakfast). Stratified random sampling is employed when there are distinct subgroups in the population that may behave differently, and it ensures that each subgroup is represented in the study. In this case, the strata are male and female participants, and random assignment within each stratum helps control for potential gender-related variables that could affect the results.

Furthermore, this design helps in comparing the effects of positive thinking across gender groups, making it a more robust experimental approach. It avoids confounding variables related to gender by ensuring an equal distribution of male and female participants in both the positive thinking and neutral task groups. The comparison of means after the SAT Math practice test provides a quantitative measure of the impact of positive thinking on cognitive ability, helping draw more meaningful conclusions about the relationship between positive thinking and academic performance.

In summary, the study is a stratified random experiment because it incorporates both stratification (based on gender) and random assignment within each stratum, allowing for a more controlled and accurate assessment of the effects of positive thinking on cognitive ability.

Answer 2

The described study fits best as a completely randomized experiment because participants were randomly assigned to two different conditions to examine the effects of an intervention on a dependent variable.

Step-by-step explanation:

The psychologist's study described in the question can be classified as ii. A completely randomized experiment. This determination is based on the fact that the participants were divided into two groups through random assignment, with one group writing about their strengths and the other group writing about their breakfast before taking the SAT Math practice test. The purpose is to compare the mean scores of both groups to determine the effects of positive thinking on cognitive ability. The study is not an observational study because the researcher is deliberately manipulating an independent variable (the task of writing down things they feel they are good at) and then measuring the dependent variable (SAT Math practice test scores). It's not a matched pairs experiment as the participants are not specifically matched in pairs, nor is it a stratified or randomized block experiment, as there are no subgroups created within each gender based on pre-existing characteristics before random assignment.