Decrease the level of significance - decrease probability of Type 1 error

CFA Level II Quant
#1

Decrease the level of significance - decrease probability of Type 1 error but increases probability of type 2 error.

Sorry, I cannot grasp this concept.

any easy way to remember this. ???

thanks

#2

this is l1 stuff.

#3

The level of significance, alpha, is defined as the probability of a Type I error. The researcher picks this value as their threshold-- the maximum acceptable probability of making a Type I error. The lower alpha is, the harder it is to reject the null hypothesis ( Note: the observed significance level is the p-value ).

A Type II error is failing to reject a false null hypothesis. If your alpha is smaller, you are less likely to reject the null hypothesis. You have made it harder to reject the null (smaller alpha), so your probability of a Type II error (failure to reject a false null) has increased.

#4

Really dislike stats so bare with me if this is explaination is only directionally accurate…

Type I errors means you incorrectly reject a true null

Type II error means you incorrectly accepting a false null

If you increase decreasey our significance level, that means you’re widening the area between mean and the critical value, which places more of the observed values into area being called statisically significant.

By doing so, you decrease the probability of rejecting a true null, but obviously there’s a chance that you’ve increased the probability of incorrectly accepting a false null

#5

The level of significance is the area in the tails of the normal probability distribution; it’s the probability that the calculated statistic will be out there (and you reject the null hypothesis) when the mean really is the hypothesized value.

#6

Based on this, you are more likely to fail to reject the null when the null is false. P(Type II error) has increased.

Also, keep in mind that there is an observed significance level and a selected significance level.

The observed significance is the p-value associated with the calculated test statistic.

The selected significance level (alpha) is the probability threshold for a Type I error and is associated with the critical value(s).

#7

Remember it this way: The P value equals (1-significance of the test). The P value is the lowest level at which you can reject the null hypothesis. Decreasing your significance increases the P value, and hence makes it harder to reject hypotheses, thus Type 1 errors (rejecting a true null hypothesis) will occur less often if your significance is lower.

#8

Haven’t seen this before, don’t think it’s correct… The observed significance level is the p-value, which is independent of the significance (alpha) level you select…

Technically, yes. More importantly, though, is that it is the probability of seeing results more contradictory to the null hypothesis (given that the null is true), than what is at hand.

Not true. Again, changing your significance (alpha) level does nothing to the observed significance of the test. One is a threshold that you select, and the other is determined by the observed test statistic.

#9

Thanks to all…

#10

Mark it for future.