Introducing Statistics: Worry About Error - AP Statistics

What is selection bias?

Bias introduced by not randomly selecting participants. Non-random participant selection creates systematic differences from the population.
What is the definition of bias in statistics?

A systematic error that occurs when a sample is not representative of the population. This creates consistent deviation from truth, making results systematically wrong.
Identify one reason to use a larger sample size.

To reduce the margin of error. More data creates narrower confidence intervals and greater precision.
Which error type can occur in a census?

Non-sampling error. Censuses eliminate sampling error but still face data collection and processing mistakes.
What is the definition of homoscedasticity?

Assumption that different samples have the same variance. Equal variance across groups is required for many statistical tests to be valid.
What is the definition of consistency in estimators?

An estimator tends to the true parameter value as sample size increases. As sample size grows, the estimator converges to the true parameter value.
What is the impact of outliers on mean?

They can skew the mean significantly. Extreme values pull the arithmetic average away from the typical center.
What is a Type I error?

Incorrectly rejecting a true null hypothesis. Also called a false positive, concluding an effect exists when it doesn't.
What is the definition of a confidence interval?

A range of values used to estimate a population parameter. Provides upper and lower bounds within which the true parameter likely falls.
What is the definition of power in hypothesis testing?

The probability of correctly rejecting a false null hypothesis. Higher power means better ability to detect true effects when present.
Which method reduces non-sampling error?

Improving survey design and data collection processes. Better procedures and training minimize errors in data collection and recording.
What is the formula for standard error of the mean?

$SE = \frac{\sigma}{\sqrt{n}}$ . Standard deviation divided by square root of sample size measures sampling variability.
What does a high standard deviation indicate?

Data points are spread out over a wider range of values. Greater variability means data points deviate more from the central tendency.
What is undercoverage in sampling?

Failing to include some members of the population in the sample. This sampling frame error excludes some members who should be included.
What is the definition of variability?

The extent to which data points differ from each other. High variability means data points are spread out rather than clustered together.
What is meant by statistical significance?

A result unlikely to have occurred by chance, given the null hypothesis. The observed difference is too large to reasonably attribute to chance alone.
What is the definition of precision in statistics?

The closeness of two or more measurements to each other. High precision means repeated measurements give very similar results.
Identify a cause of selection bias.

Convenience sampling. Choosing easily accessible participants often creates unrepresentative samples.
Identify one method to detect outliers.

Use box plots or z-scores. Visual and statistical methods identify unusually extreme data points.
What is the role of p-value in hypothesis testing?

Indicates the probability of observing the data if the null hypothesis is true. Lower p-values provide stronger evidence against the null hypothesis.
What is the definition of heteroscedasticity?

Different samples have different variances. Unequal variances violate assumptions of many standard statistical procedures.
Identify a consequence of measurement error.

Biased estimates of population parameters. Inaccurate measurements lead to systematically incorrect parameter estimates.
What is a Type II error?

Failing to reject a false null hypothesis. Also called a false negative, missing an effect that actually exists.
What is the definition of a sampling error?

The difference between a sample statistic and a population parameter. This represents the natural variation between sample statistics and true population values.
What is the definition of a non-sampling error?

Errors not related to the act of sampling, such as data entry errors. These systematic mistakes affect data quality regardless of sampling method used.
What is the formula for confidence interval for a mean?

$\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$ . Sample mean plus/minus margin of error based on standard error.
What is the definition of reliability in statistics?

The consistency of a measure or test over time. Reliable measures produce consistent results when repeated under same conditions.
Which error type is unavoidable in sampling?

Sampling error. Random variation always exists when using samples instead of entire populations.
Identify one strategy to minimize Type II errors.

Increase the sample size. More data improves power to detect true effects when they exist.
Identify one strategy to minimize Type I errors.

Lower the significance level ( $\alpha$ ). Stricter criteria reduce the chance of false positive conclusions.
What does it mean if a statistic is unbiased?

The expected value of the statistic is equal to the true parameter. No systematic over- or under-estimation occurs on average across samples.
Identify one way to reduce sampling error.

Increase the sample size. Larger samples provide more accurate estimates by reducing random variation.
Identify one cause of response bias.

Leading questions in a survey. Questions that suggest desired answers influence how respondents reply.
What is the definition of overcoverage?

Including members not part of the population of interest in a sample. This sampling frame error includes units that shouldn't be in the target population.
What is the effect of increasing confidence level on interval width?

Increases the width of the confidence interval. Higher confidence requires wider intervals to maintain the stated certainty level.

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