Question

Can the standard error be a negative (no. 8). Is it possible to check the others

For each of the following, circle your answer to indicate whether the quantity can NEVER be negative or can SOMETIMES be negative:

1	z-score	Sometimes	Never
2	Probability	Sometimes	Never
3	Test statistic	Sometimes	Never
4	Sample proportion	Sometimes	Neverþ
5	Standard deviation	Sometimes	Never
6	Sum of squares	Sometimes	Never
7	Standard error	Sometimes	Never
8	p-value	Sometimes	Never þ
9	Correlation coefficient	Sometimes	Never
10	χ² value	Sometimes	Never þ

Answer 1

1. Z score - Sometimes , if the observation is less than mean then Z score is negative.

2. Probability- Never , because range of probability is 0 to 1.

3. Test statistic - Sometimes , Z statistic,t statistic can be negative.

4. Sample proportion- Never, proportion is number of success divided by total number of samples. This can't be negative

5. Standard deviation- Never , Standard deviation is positive square root of the Variance.

6. Sum of squares - Never , squares are always positive term. And sum of them are also positive.

7. Standard error - Never , standard error depends on only standard deviation(sd) and sample size n , , sd and n are both positive terms. So standard error is also positive.

8. P value - never , p value is a probability quantity and a probability never be negative.

9. Correlation coefficient - Sometimes , If relationship between two variables is negative that means if one increases other decreases, then the correlation coefficient between them is negative.

10. Chi square value - Never , because it is the sum of squares of difference between the observed and expected frequencies.