Question

How do we know the answer for that? The answer is 6.

You perform a Q-test on a particular data point and obtain a Q value of 0.67. How many data points would you need to be able to reasonably discard this data point as erroneous?

Answer 1

The limit values of the two-tailed Dixon's Q test can be summarized using the following table

The number of values:	3	4	5	6	7	8	9	10
Q90%:	0.941	0.765	0.642	0.560	0.507	0.468	0.437	0.412
Q95%:	0.970	0.829	0.710	0.625	0.568	0.526	0.493	0.466
Q99%:	0.994	0.926	0.821	0.740	0.680	0.634	0.598	0.568

So we basically compare the calculated Q value with the table value mentioned above.

Since you have not specified the level of confidence, I am assuming it to be 95%.

The data points we would need to be able to reasonably discard this data point as erroneous would be the data point at which Q < Q_table

At Q = 0.67 < Q₆(table) = 0.625

At Q = 0.67 > Q₇(table) = 0.710

Hence at 95% level of confidence the number of data points is 6 at which we would be able to reasonably discard this data point as erroneous.
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