Which statement describes a difference between sample standard deviation (SD) and the standard error of the mean (SEM)? OSD measures how data points differ from the sample mean. SEM measures how the sample mean differs from the population mean. OSD describes a unitless value but SEM has the same units as the data. The value of SD is always smaller than the value of SEM for any sample population. Studies that include more sample measurements have lower values of SD. SEM does not change when the sample size increases.

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### Understanding the Difference between Sample Standard Deviation (SD) and Standard Error of the Mean (SEM)

**Question:**

Which statement describes a difference between sample standard deviation (SD) and the standard error of the mean (SEM)?

1. ❍ **SD measures how data points differ from the sample mean. SEM measures how the sample mean differs from the population mean.**

2. ❍ **SD describes a unitless value but SEM has the same units as the data.**

3. ❍ **The value of SD is always smaller than the value of SEM for any sample population.**

4. ❍ **Studies that include more sample measurements have lower values of SD. SEM does not change when the sample size increases.**

**Correct Answer:**

3. ❍ **The value of SD is always smaller than the value of SEM for any sample population.**

### Detailed Explanation:

- **Option 1:** Incorrect. Both SD and SEM are in the same units as the data and none measure specifically how the sample mean differs from the population mean. SEM measures the precision with which the sample mean estimates the population mean.

- **Option 2:** Incorrect. Both SD and SEM have the same units as the data, and neither are unitless.

- **Option 3:** Correct. This option is incorrect in terms of its classical understanding. Typically, SEM is smaller than or equal to SD as it is the SD divided by the square root of the sample size. In specific cases where sample size is 1, SEM would be equal to SD.

- **Option 4:** Incorrect. SEM decreases as the sample size increases, but SD may or may not decrease as it is more influenced by the variability in the data.

This question helps in understanding the differences and applications of SD and SEM in statistical analysis.
Transcribed Image Text:### Understanding the Difference between Sample Standard Deviation (SD) and Standard Error of the Mean (SEM) **Question:** Which statement describes a difference between sample standard deviation (SD) and the standard error of the mean (SEM)? 1. ❍ **SD measures how data points differ from the sample mean. SEM measures how the sample mean differs from the population mean.** 2. ❍ **SD describes a unitless value but SEM has the same units as the data.** 3. ❍ **The value of SD is always smaller than the value of SEM for any sample population.** 4. ❍ **Studies that include more sample measurements have lower values of SD. SEM does not change when the sample size increases.** **Correct Answer:** 3. ❍ **The value of SD is always smaller than the value of SEM for any sample population.** ### Detailed Explanation: - **Option 1:** Incorrect. Both SD and SEM are in the same units as the data and none measure specifically how the sample mean differs from the population mean. SEM measures the precision with which the sample mean estimates the population mean. - **Option 2:** Incorrect. Both SD and SEM have the same units as the data, and neither are unitless. - **Option 3:** Correct. This option is incorrect in terms of its classical understanding. Typically, SEM is smaller than or equal to SD as it is the SD divided by the square root of the sample size. In specific cases where sample size is 1, SEM would be equal to SD. - **Option 4:** Incorrect. SEM decreases as the sample size increases, but SD may or may not decrease as it is more influenced by the variability in the data. This question helps in understanding the differences and applications of SD and SEM in statistical analysis.
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