Survey Experiment Observational Studies and Survey To gather

Survey, Experiment, Observational Studies, and

Survey • To gather information by individual samples so as to learn about the whole thing. • A Survey measures a characteristic of interest. Example: You can do a survey on people’s opinions, by asking randomly chosen people the same questions.

Experiment An experiment applies a treatment (a condition administered) to experimental units to observe an effect.

• A completely randomized design implies that all experimental units have the same probability of being selected for application of the treatment. • A randomized block design involves first grouping experimental units according to a common characteristic, and then using random assignment within each group. • A matched pairs design involves creating blocks that are pairs. In each pair, one unit is randomly assigned the treatment. Sometimes, both treatments may be applied, and the order of application is randomly assigned.

Observational Studies • In an observational study, a researcher observes and records measurements of variable of interest but does not impose a treatment. • The results of an observational study can only imply an association. The results of an experiment, by imposing a condition, can imply causation. • An observational study looks for an association between a factor and characteristic of interest.

Lurking and Confounding Variables Confounding Variable is a third unmeasured variable that may be associated with both of the measured variable. This variable is “confounded with” one of the other two, and therefore is a potential explanation of the association A Lurking Variable is a variable that is not included as an explanatory or response variable in the analysis but can affect the interpretation of relationships between variables. A lurking variable can falsely identify a strong relationship between variables or it can hide the true relationship. A Lurking Variable is a variable that is Not considered in a research study that could influence the relations between the variables in the study. A confounding variable is a variable that is considered in a research study that could influence the relations between the variables in the study. A Lurking Variable is not taken into account by the researches while a confounding variable is taken into account by the researchers. Both are variables that could influence the relations between the variables of primary interest in a research study.

Examples Online Assessments A professor is teaching an online course that requires weekly homework assignments and weekly quizzes. She wants to know if there is a relationship between students’ homework and quiz grades. She makes a graph showing students’ scores on the two assessments. After she starts looking at the data she realizes that the days when students submit their assignments may play a role in their grades on these assignments. Students who wait until the night the assignment are due tend to have lower scores than those who submit a day or two before the deadline. She uses this information to change her analyses to include the submission time. Originally submission time was a lurking variable because the professor was not including it in her study. Now that she is including this variable in her study it is a confounding variable. Weight Comparisons A student is conducting a research study on differences in body weight between engineering and nursing students at Penn State. His data show that engineering students weight more than nursing students on average. Then, his advisor points out that Penn State’s College of Engineering is 81. 1% male while the Penn State’s College of Nursing is 7. 7% male. The student conduct a second research study and includes biological sex. He finds that there is not a different between engineering and nursing students after controlling for biological sex. In the first study gender was a lurking variable because the students was not taking it into account. In the second study gender was a confounding variable because the student was taking it into account. Note that the results of the study changed when biological sex was taken into account.

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Margin of Error • The margin of error is the range about the sample proportion in which you would expect to find the actual population proportion. • The margin of error indicates how close the actual proportion is to the estimate of the proportion found in a survey of a random sample. Example

• Sampling Distribution is the distribution of proportions of those who indicate they are satisfied for all possible samples of size n from the population.

Normal Condition • As sample sizes increase, the sampling distribution becomes more and more normal. If a random sample of sizes n has a proportion of successes p, there are two conditions that, if satisfied, allow the distribution to be considered approximately normal. Those two conditions are P = The sample proportion (the proportion of successes) for the random sample n = The number of subjects in the random sample.

Standard Deviation of a Sample Proportion • It represents the average distance of a sample proportion from the actual proportion. • It’s the spread or variation from the actual population proportion. Formula: P = The sample proportion (the proportion of successes) for the random sample n = The number of subjects in the random sample.

Calculate Margin of Error • The margin of error is found by multiplying the standard deviation by the critical value. • A critical value for an approximately normal distribution is the z-score that corresponds to a level of confidence.

Example The Gallup-Healthways Well-Being Index tracks, on a daily basis, the proportion of Americans who say they experienced happiness and enjoyment without stress and worry on the previous day. On one particular day, the survey of 500 people indicated that 54% were happy, with 95% confidence that the margin of error is ± 4 percentage points. • The sample proportion is 0. 54. • Since np > 10, 500(0. 54) = 270 > 10, and n(1 – p) > 10, 500(1 – 0. 54) => 500(0. 46) 10 we can assume that the sample distribution is approximately normal.

Example In late 2011 the Gallup organization surveyed a random sample of 2007 American adults and asked them what they thought about China’s relationship with the United States. 76% of those surveyed said that China was either “friendly” or “an ally”. Gallup reported the following statement along with the surveyed results: For results based on the total sample size of 2007 adults, one can say with 95% confidence that the margin of error attributable to sampling and other random effects is ± 1. 87 percentage points.