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Standard error of the mean and confidence intervals

How precise is the sample estimate, judged from its standard error and interval?

More, if you want it

Outcomes (5)

Tell the from the by whether it describes single scores or sample means.
Tell the from the by dividing the SD by the square root of .
Tell a from a by the number of standard errors on each side.
Tell a 90% confidence interval from a by its narrower line from the same data.
Name the when one interval line on a chart is the longest.

What does the patient want to know about the spread in the results?Tap a term: its definition, what you can do with it, and how often the exam asks it.

spread of scores

standard deviation§1The patient hears "scores spread about 10 points from the average"
Definition: the spread of single scores around their mean.
You can: Tell the standard deviation from the standard error of the mean by whether it describes single scores or sample means.
Must knowAsked 3×

spread of averages

standard error of the mean§1The patient hears "the average could be about 1 point out"
Definition: the spread of single scores around their mean.
You can: Tell the standard deviation from the standard error of the mean by whether it describes single scores or sample means.
Must knowAsked 3×
95% confidence interval§3The patient hears "the true average is probably between 257 and 267"
Definition: the mean plus or minus about 2 standard errors.
You can: Tell a 95% confidence interval from a 90% confidence interval by the number of standard errors on each side.
Must knowAsked 4×
90% confidence interval§4The patient says "I want a shorter range from the same data"
Definition: a shorter interval from the same data, lying inside the 95% one.
You can: Tell a 90% confidence interval from a 95% confidence interval by its narrower line from the same data.
Must knowAsked 1×

interval chart

least precise estimate§5The patient hears "the ward with 1 to 13 has the longest line"
Definition: the mean with the widest interval, often from a small or variable sample.
You can: Name the least precise estimate when one interval line on a chart is the longest.
Must knowAsked 1×

Each card is one term. The grey line is what the patient says, which is what the question stem gives.

Summary

: the spread of single scores around their mean.
: the of sample means, equal to SD divided by the square root of .
: the mean plus or minus about 2 standard errors.
: a shorter interval from the same data, lying inside the 95% one.
: the mean with the widest interval, often from a small or variable sample.

Standard deviation

Must knowAsked 3×5 s

The standard deviation (SD) shows how spread out single scores are around their mean.

Spread of single scoresDefinitionMustAsked 3×10 s

The standard deviation (SD) shows how spread out single scores are around their mean. A ward sample with SD 10 has scores spread about 10 points from the mean.

Ward audit scoresPatient exampleShouldAsked 3×10 s

Priya is a charge nurse who collects anxiety scores on an acute ward. Priya says, "Most patients score within about 10 points of the ward average."

Two numbers in one reportCompareMustAsked 3×5 s

The SD describes single patients, and the standard error describes the group mean.

More: Group results in papersNice to know13.8.715 s

The standard error is a separate statistic. Papers report the standard error alongside group results, for the group mean. A study can report a control group's SD for single scores. The same study can give a standard error in brackets for another group's mean.

6 more sections on Standard error of the mean and confidence intervals

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