Deck 13: Uncertainty of Numeric Estimates

Question 1

Why does sampling from a population introduce uncertainty into the sample estimates?

A) variation in samples drawn from the population
B) systematic error in samples drawn
C) changes in population due to time
D) estimates different from population statistics

Answer 1

A

Question 2

What is a point estimate?

A) estimate of a sample parameter
B) estimate of a population parameter
C) mean of several sample means
D) variance of a population parameter

Answer 2

B

Question 3

Why is inferential statistics from a sample collected using nonprobability methods problematic?

A) Sample has both sample and systematic error.
B) sample not representative of the population
C) Sample data is incomplete or partially missing.
D) Sample has too many outlier values.

Answer 3

B

Question 4

The sample mean of a variable is found to be 35.7. The true population mean of that variable was known to be 40.2. What is the sampling error of the variable?

A) 4.20
B) 9.00
C) 4.50
D) 2.25

Question 5

Three different samples were drawn from a population. The mean of variable AGE for the three samples was found to be 24, 27, and 21, respectively. What is the sampling variation in AGE?

A) 3.0
B) 8.0
C) 9.0
D) 1.5

Question 6

What are the two factors that determine the standard error of a point estimate?

A) population size and sample size
B) sample estimate and population statistic
C) standard deviation and variance of estimate
D) sample size and variance of estimate

Question 7

The sample mean of the variable height in a data set was found to be 68 inches, with a standard error of four inches. The researcher reported that the population or true mean height fell within one margin of error of the sample mean, at the 95% confidence level. What is the chance that the true mean is 75 inches or more?

A) 95%
B) 2.5%
C) 5%
D) 47.5%

Question 8

What is a confidence interval of a point estimate?

A) the likelihood that the true parameter falls within a range of values
B) the values that the true parameter is likely to exceed, at a given level
C) a numeric range within which the true parameter falls, at a given confidence level
D) a percentage range of the likelihood that the sample and true mean are equal

Question 9

Which of the following is not affected by sample size?

A) random error
B) bias
C) uncertainty
D) reliability

Question 10

How could bias be reduced, if measurement validity has been corrected?

A) take a representative sample
B) increase the sample size
C) ensure measurement reliability
D) choose a different population

Question 11

What is hypothesis testing?

A) assess whether a point or sample estimate falls within a given confidence interval
B) confirm a hypothesis that a population parameter has a given p value
C) state an assumption on the expected value of a sample estimate
D) assess whether a hypothesis on a population parameter is supported by sample data

Question 12

The sample mean of a variable is 137.6, and is reported with an associated p value of 0.001. How could this p value be interpreted as?

A) Probability of .999 that true mean is null, when sample mean is 137.6.
B) The chance of the population or true mean being 137.6 is 0.001.
C) Probability of .001 that population mean is 0, when sample mean is 137.6.
D) 99.9% chance that the true mean is greater than 137.6.

Question 13

If the p value of the hypothesis test in Question 13 is calculated to be .003, what conclusion could be made from the test?

A) Estimate is not significant.
B) Population parameter is null.
C) Estimate is statistically significant.
D) accept the null hypothesis

Question 14

In a research study the estimate of variable X is found to be 12.8, with a confidence interval of 10.8 and 14.8. A second estimate of variable X, using a different sample, was 14.2, with a confidence interval of 11.2 and 17.2. What can we say about the difference in the two estimates, if both had valid p values? Choose the best answer.

A) Difference is not significant.
B) Difference is statistically significant.
C) Any difference cannot be determined.
D) There is minimal difference.

Question 15

What is an alternative term used in recent research for "confidence interval"?

A) confidence bounds
B) significance interval
C) compatibility interval
D) reliability range

Question 16

What is the current critique of a statistically significant estimate found using traditional research methods?

A) Estimate is biased downwards.
B) Estimate significance is often unknown.
C) Estimate is different for other p values.
D) Estimate is biased upwards.

Question 17

What is a common critique of traditional research methods of testing significance, other than publication bias? Choose the best answer.

A) incorrect statistical techniques
B) misleading conclusion on presence of a null effect
C) misleading usage of a confidence interval
D) erroneous calculation of the point estimate

Question 18

What could be done to minimize faulty inferences made with traditional research methods? Choose the best answer.

A) remove references to confidence intervals of estimate
B) choose multiple p values for testing significance
C) report compatibility interval along with estimate
D) interpret direction, size, and uncertainty of estimate

Question 19

What is meant by publication bias? Choose the best answer.

A) an upward bias in effect sizes of estimates
B) a bias toward medical research papers
C) a downward bias in effect size of estimate
D) publication of research with yes/no conclusions

Question 20

What does the value of 'R' represent in a correlation matrix for bivariate data?

A) the p values of each pair of variables
B) correlation of a variable with itself
C) strength of association between two variables
D) the number of cases with values for both variables

Question 21

A cell in a bivariate correlation matrix shows a value of 1 for the 'R' statistic. How would you interpret this value?

A) positive correlation present
B) one case with both variable values
C) incorrect p value in the table
D) correlation of a variable with itself

Question 22

What is the statistical measure generally shown in a cross-tabulation between two categorical variables?

A) R²
B) R
C) ᵪ²
D) variance

Question 23

What is a multichotomous variable?

A) a numeric variable with multiple decimals
B) a categorical variable with one or more categories
C) an interval variable with one or more values
D) a categorical variable with two or more categories

Question 24

Which measure is used to analyze difference in means in an ANOVA test?

A) R²
B) F statistic
C) standard deviation
D) ᵪ²

Question 25

"Statistical uncertainty" means a sample estimate can never be exactly equal to the population parameter.

Question 26

Inferential statistics means reaching a conclusion about characteristics of a population based on sample data.

Question 27

A "point estimate" is a summary statistic, such as the mean or proportion, of the population.

Question 28

The mean income of residents of Long Island City, NY, was $32,500. The mean income of a random sample of 200 residents of Long Island City was found to be $28,900. The difference between the two numbers ($3,600) is known as sampling error.

Question 29

The higher the precision of a sample estimate, the lower is its sampling error.

Question 30

The standard error is an estimate of the sampling error of a point estimate.

Question 31

The sample size drawn from a population was increased from 200 cases to 1,000 cases. This increase in sample size reduced the standard error of summary statistics calculated from the independent variable in the data.

Question 32

Choosing a higher confidence level results in a smaller range for margin of error of a sampling estimate.

Question 33

A confidence level of 99% is interpreted as the difference between a sample estimate and the population parameter is less than the margin of error 99% of the time.

Question 34

A confidence interval is calculated as Point Estimate (+/-) 2*Margin of Error.

Question 35

What are the limits, if any, to values of uncertainty measures such as standard error, confidence level, and confidence interval?

Question 36

Distinguish between random error and bias. Illustrate the differences with the help of an example.

Question 37

Describe the steps in developing a hypothesis test. Walk through these steps with an example.

Question 38

Write a hypothesis statement on cigarette smoking and the probability of cancer as the variables of interest. You may have 2 statements for the null and the alternative hypothesis respectively.

Question 39

Explain what is a p value, and how it is used in hypothesis testing. Provide an example.

Question 40

In a hypothesis test, a significance level of 0.05 was chosen. How would you interpret this value?

Question 41

Explain what is a 'statistically significant' result from a hypothesis test. Illustrate with an example.

Question 42

With the help of an example, illustrate how confidence intervals could be used to assess differences in an outcome variable across values of a categorical independent variable.

Question 43

Distinguish between interpreting a confidence interval and a compatibility interval.

Question 44

In your own words, describe what is 'publication bias'. Provide an example.

Question 45

Find a research paper on the internet that uses traditional statistical hypothesis testing and reports on measures of uncertainty. Identify the inferential statistics and uncertainty measures used in the study. Comment on these statistics and measures.

Question 46

Using the paper chosen in question 1, comment on the hypothesis development and testing done by the authors. Would you have done anything differently in this process of hypothesis testing?

Question 47

Discuss any drawbacks you observe in the traditional statistical methods used by the authors of the paper in question 1. How would you revise the approach taken by the authors on significance testing, using more current approaches? Explain your answer.