| A | B |
|---|
| True/False: By definition, a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection. | False |
| True/False: Clusters are non-overlapping subgroups of a population that have been identified as homogeneous. | False |
| True/False: Blocking is a technique that can be used to filter out the effects of extraneous factors. | True |
| True/False: Response bias can occur when responses are not actually obtained from all individuals selected for inclusion in the sample. | False |
| True/False: Selection bias can occur if volunteers only are used in a study. | True |
| True/False: Stratified sampling is a sampling method that in no way involves simple random sampling. | False |
| True/False: Increasing sample size will generally eliminate bias in a sample. | False |
| True/False: A placebo is identical in appearance to the treatment of interest, but contains no active ingredients. | True |
| True/False: A study is an observational study if the investigator observes the behavior of a response variable when one or more factors are manipulated. | False |
| True/False: In a well-designed experiment, the factors are confounded whenever possible. | False |
| True/False: As long as the sample size is small relative to the population, there is little practical difference between sampling with replacement and sampling without replacement. | True |
| True/False: A treatment is any particular combination of values for the explanatory variables. | True |
| True/False: Two factors are extraneous if their effects on the response variable cannot be distinguished from one another. | False |
| True/False: Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes. | False |
| True/False: The method of control wherein an extraneous variable is held constant is called blocking. | False |
| True/False: A control group provides a baseline for comparison to a treatment group. | True |
| True/False: Random assignment of volunteers should result in comparable experimental groups. | True |
| True/False: If the subjects as well as the person measuring the response are aware of the treatment assigned to the subject, only single-blinding is being used. | False |
| True/False: Replicating in an experiment means that the number of subjects is greater than 1. | True |
| True/False: Subpopulations of a population are called strata. | True |
Bias is a serious problem that sometimes arises when one takes a sample.
a) In a few sentences, explain what bias is.b) What is the difference between selection bias and non-response bias? | Bias is the tendency for a sample to differ from the corresponding population in some systematic way. Selection bias occurs when some part of the population is systematically excluded from the sample. However, non-response bias occurs when responses are not actually obtained from the individuals who were selected for the sample. |
| Suppose that two experiments were conducted to compare the effects of two new insect repellants. In Experiment X, a simple random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. In Experiment Y, a stratified random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. (River City has 4 geographic areas of town, the NE, NW, SE, and SW quadrants; 100 people from each quadrant were sampled for Experiment B.) The results of the experiments were the same: fewer insects landed on the arms that had been treated with insect repellant A. a) Can one infer from each of these experiments that repellant A is better than B? Why or why not? b)Can one generalize to the population of River City from each of these experiments? Why or why not? | In each of these experiments we can infer a cause-and-effect relationship because the volunteers were randomly assigned to the two treatments. In each of these experiments, we can generalize the results of the experiment to the population of River City since the subjects were randomly selected from the population of River City. Thus, the subjects should be representative of the population in general. |
| In response to Press reports about music companies inserting secret messages in their recordings, an experiment was conducted. The study attempted to examine the role of suggestion in perceiving "messages" in rock-and-roll recordings presented backward. (The music had been recorded backward by a stereo system with a reel-to-reel tape recorder, and then re-recorded to a cassette player.) The stimuli consisted of three rock-and-roll songs: "Revolution No. 1," by the Beatles; "Stairway to Heaven" by Led Zeppelin; and "Black Sabbath" by Black Sabbath. Subjects for the experiment were volunteers from introductory psychology classes, and were randomly assigned into one of three groups. Those assigned to Group I (the control group) were told to listen to the music and write down any reactions. The Group II members were asked to listen and write down any words or phrases they heard, but were not given any hints about the possible content. Members of Group III were told that messages had been recorded, and that their task was to detect the messages and write them down. All subjects in each Group listened to the same songs in the same order. In the resulting analysis it was found that the members of Group III claimed they heard more phrases than the members of Group II, and the members of Group II claimed they heard more phrases and words than the Group I members. a) What is the explanatory variable (factor) for this experiment? b) What is the response variable for this experiment? c)In questioning after completing the study, if was found that 80% of the subjects in Groups II and III had read recent reports in the newspaper that music companies had inserted messages in recordings. Only 33 % of the individuals in Group I (the controls) had read of this in the Press. How does this information affect the interpretation of the results? | The explanatory variable is the directions provided to each group. The response variable is the number of phrases heard. Reading of this in the press is a potential confounding variable since it is related both to group membership and to the response variable. For example, the subjects in Group I may have heard less phrases because of the information provided (explanatory variable) or because fewer of the subjects were aware of the controversy. Thus, it may not be a good idea to attribute the results entirely to the power of suggestion. |
| In response to Press reports about music companies inserting secret messages in their recordings, an experiment was conducted. The study attempted to examine the role of suggestion in perceiving "messages" in rock-and-roll recordings presented backward. (The music had been recorded backward by a stereo system with a reel-to-reel tape recorder, and then re-recorded to a cassette player.) The stimuli consisted of three rock-and-roll songs: "Revolution No. 1," by the Beatles; "Stairway to Heaven" by Led Zeppelin; and "Black Sabbath" by Black Sabbath. Subjects for the experiment were volunteers from introductory psychology classes, and were randomly assigned into one of three groups. Those assigned to Group I (the control group) were told to listen to the music and write down any reactions. The Group II members were asked to listen and write down any words or phrases they heard, but were not given any hints about the possible content. Members of Group III were told that messages had been recorded, and that their task was to detect the messages and write them down. All subjects in each Group listened to the same songs in the same order. In the resulting analysis it was found that the members of Group III claimed they heard more phrases than the members of Group II, and the members of Group II claimed they heard more phrases and words than the Group I members. a)What is the explanatory variable (factor) for this experiment? b)What is the response variable for this experiment? c) In questioning the subjects after completing the study, it was found that 80% of the subjects in Groups II and III had read recent reports in the newspaper that music companies had inserted messages in recordings. Only 33 % of the individuals in Group I (the controls) had read of this in the Press. How does this information affect the interpretation of the results? | The explanatory variable is the directions provided to each group.; The response variable is the number of phrases heard. Reading of this in the press is a potential confounding variable since it is related both to group membership and to the response variable. For example, the subjects in Group I may have heard less phrases because of the information provided (explanatory variable) or because fewer of the subjects were aware of the controversy. Thus, it may not be a good idea to attribute the results entirely to the power of suggestion. |
| Suppose that two experiments were conducted to assess the effect of a new insect repellant. In Experiment A, a simple random sample was taken from the population of River City. In Experiment B, a simple random sample from a group of volunteers from the population of River City was used. The results of the experiments were the same: fewer insects landed on the arms that had been treated with the insect repellant. The volunteers were randomly assigned to the two treatments in both experiments. a) Can one infer a cause-and-effect relation between the use of the repellant and fewer insects landing from each of these experiments? Why or why not? b)Can one generalize to the population of River City from each of these experiments? Why or why not? | In each of these experiments we can infer a cause-and-effect relationship because the volunteers were randomly assigned to the two treatments.; In experiment A, we can generalize the results of the experiment to the population of River City since the subjects were randomly selected from the population of River City. Thus, the subjects should be representative of the population in general. However, in experiment B, the random sample came from a group of volunteers from River City, who may not be representative of the general population of River City. |
| In competitive sports, video recorders have been used more frequently in recent years. The idea behind the recorder is that coaches can replay the training sessions for more effective feedback to the athlete. Some people believe video recording may make the athletes more nervous and actually decrease their performance. You have been asked to design an experiment to address this issue for competitive high school tennis players. You have decided to use the accuracy of tennis serves as your response variable, and the number of successful serves out of 100 as your performance measure. The subjects for your experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment. a) Describe the treatments in your experiment. b)One possible confounding variable is the experience levels of the players. What method would you use to control this variable? c) Do you feel the results of this experiment could be generalized to all male? | The two treatments will be: 1. The subject is recorded and 2. The subject is not recorded.; I would use blocking (pairing) to control the experience level of players. I would pair the two most experienced together as one block, the next two most experienced as the next block, and so on. Then the two members of each block would be randomly split into the two treatment groups.; No, the results of this study should not be generalized to all male tennis players for at least two reasons. One, competitive tennis players are presumably more used to playing in front of crowds and would be less bothered by video recording than the typical player. Two, volunteers are not generally representative of any larger population. Note: either reason should be sufficient to receive credit. |
| The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n? | A simple random sample of size n is a sample that is selected from a population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. |
| A friend of yours, who is not taking statistics, wonders why it is that anyone would choose to take a sample. "Obviously," he says, "you would get better information from a census." In a short paragraph, explain why it is that statisticians take a sample rather than a census. | Although we may get better information from a census, it is usually far too costly and time consuming to contact every member of the population. A large random sample will be nearly as good for far less cost. |
| The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n? | A simple random sample of size n is a sample that is selected from a population in a way that ensures that every different possible sample of the desired size has the same chance of being selected. |
| We have distinguished two types of studies: observational and experimental. Briefly explain the essential difference(s) between these two types of study. | In an experiment, researchers observe how a response variable behaves when they manipulate one or more factors. However, in an observational study, the researchers do not manipulate any factors. Instead, they observe characteristics of a subset of the members of one or more existing populations. |
| In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable? | In an experiment, the explanatory variable is the one that researchers manipulate in order to observe changes in the response variable. An extraneous variable is any other variable which is thought to affect the response variable, but is not of interest in the study. |
| Bias, the tendency for samples to differ from the corresponding population in some systematic way, might be due to: (a) selection bias, (b) response bias, and/or (c) nonresponse bias. In a few sentences, discuss the differences among these different biases. | Selection bias occurs when some part of the population is systematically excluded from the sample. Non-response bias occurs when responses are not actually obtained from all individuals who were selected for the sample. With response bias, however, responses are obtained from the subjects, but the method of observation tends to produce values that systematically differ from the true population value in some way. |
| The following paragraph describes an actual study. After reading the description, determine whether the study is an observational or experimental study. Justify your answer with specific references to the information in the study. | This is an experiment since there was a planned intervention undertaken to observe the effects of an explanatory variable (the letter on the cup) on a response variable (cup preference). |
| Three methods for random sampling are: (a) simple random sampling, (b) stratified random sampling, and (c) cluster sampling. In a few sentences, discuss the similarities and differences among these sampling methods. Specifically, what sampling circumstances would lead you to choose each of these methods? | In simple random sampling, every individual and every possible sample of size n has an equal chance of being selected for the study. In stratified random sampling, the population is divided into non-overlapping homogeneous groups (called strata) and a simple random sample is selected from each strata. In cluster sampling, the population is divided into non-overlapping (preferably heterogeneous) groups called clusters and then a random sample of clusters is selected and every member of the selected clusters is studied. Cluster sampling works best when the population is already divided into easily identifiable groups that are heterogeneous (i.e. each cluster can reasonably be assumed to be representative of the entire population). Stratified random sampling works best when there are easily identified groups in the population that are anticipated to have very different responses to the question of interest. Simple random sampling is best when neither of the circumstances listed above are present. |
| Under what conditions is a stratified random sample preferable to a simple random sample? | When the population has well defined sub-populations. |
| Briefly explain why it is important to control for extraneous factors in an experiment. | So that we can determine the effects of the relevant factors on the response variable. |
| A large university's college recruiter is going to study the starting salaries of the university's graduates. What might the college recruiter use as strata, when drawing a stratified random sample, in order to obtain the most accurate information concerning the starting salary of this university's graduates? | Major (other answers are possible). |
| Briefly explain why the subjects in an experiment should be randomly assigned to the experimental (or treatment) groups. | Randomization ensures that the experiment does not intentionally favor one experimental condition over any other. |
| Briefly explain what it means when two factors are said to be confounded. | Their effects on the response variable cannot be distinguished from one another. |
| A botanist is studying the number of flowers produced by a certain type of houseplant when subjected to three different levels of fertilizer. Determine the response variable and the factor that determines the experimental conditions in this experiment. | The response variable is the number of flowers, and the experimental factor is fertilizer. |
