Introducing Statistics: Worry About Error - AP Statistics

The difference between a sample statistic and a population parameter. This represents the natural variation between sample statistics and true population values.

Increase the sample size. Larger samples provide more accurate estimates by reducing random variation.

Errors not related to the act of sampling, such as data entry errors. These systematic mistakes affect data quality regardless of sampling method used.

Non-sampling error. Censuses eliminate sampling error but still face data collection and processing mistakes.

A systematic error that occurs when a sample is not representative of the population. This creates consistent deviation from truth, making results systematically wrong.

$SE = \frac{\sigma}{\sqrt{n}}$. Standard deviation divided by square root of sample size measures sampling variability.

Improving survey design and data collection processes. Better procedures and training minimize errors in data collection and recording.

Biased estimates of population parameters. Inaccurate measurements lead to systematically incorrect parameter estimates.

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.

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

Lower the significance level ($\alpha$). Stricter criteria reduce the chance of false positive conclusions.

Increase the sample size. More data improves power to detect true effects when they exist.

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

Sampling error. Random variation always exists when using samples instead of entire populations.

The extent to which data points differ from each other. High variability means data points are spread out rather than clustered together.

Convenience sampling. Choosing easily accessible participants often creates unrepresentative samples.

Data points are spread out over a wider range of values. Greater variability means data points deviate more from the central tendency.

The probability of correctly rejecting a false null hypothesis. Higher power means better ability to detect true effects when present.

An estimator tends to the true parameter value as sample size increases. As sample size grows, the estimator converges to the true parameter value.

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

Assumption that different samples have the same variance. Equal variance across groups is required for many statistical tests to be valid.

Use box plots or z-scores. Visual and statistical methods identify unusually extreme data points.

Different samples have different variances. Unequal variances violate assumptions of many standard statistical procedures.

They can skew the mean significantly. Extreme values pull the arithmetic average away from the typical center.

A range of values used to estimate a population parameter. Provides upper and lower bounds within which the true parameter likely falls.

Use box plots or z-scores. Visual and statistical methods identify unusually extreme data points.

A range of values used to estimate a population parameter. Provides upper and lower bounds within which the true parameter likely falls.

Non-sampling error. Censuses eliminate sampling error but still face data collection and processing mistakes.

Improving survey design and data collection processes. Better procedures and training minimize errors in data collection and recording.