Null hypothesis / is there a wolf present?

[lammy]

Hypothesis testing makes my head spin like the possessed girl on The Exorcist!!!

Say my null hypothesis = there is no wolf present, then

false null hypothesis = there is a wolf present?

and rejecting a false null hypothesis = believing that there is no wolf present?

and failing to reject a false null hypothesis = believing there is a wolf present?

I think failing to reject a false null hypothesis is a Type II error which means that I believe there is no wolf present when there is a wolf around ??? which is opposite of my logic above.

Related to the t-test, if n increases, I’m more likely to reject a false null hypothesis. If n increases, isn’t my t-stat increasing so it’s more likely to be greater than my t-critical and I accept the null as being true? Why is that bad?

I hope stats is only 5% of the exam!!!

[Rasec]

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a “false positive”), while a type II error is the failure to reject a false null hypothesis (a “false negative”)

[tickersu]

@lammy

Hypothesis testing makes my head spin like the possessed girl on The Exorcist!!!

Say my null hypothesis = there is no wolf present, then

false null Alternative hypothesis = there is a wolf present? Your alternative hypothesis (Ha) would be that a wolf is present (given that you said the null is that no wolf is present).

and rejecting a false null hypothesis = believing that there is no wolf present? No– Break this down in the words of your problem. Your null is that no wolf is present, and you are saying this is false. So, this means that the true state is a wolf is present. You have said we reject the idea that no wolf is present, meaning we think a wolf is present. In totality, we believe there is a wolf, and in truth, there is a wolf (we made the correct decision to reject the null when it is false).

and failing to reject a false null hypothesis = believing there is a wolf present? No–** again, break it down. You say that, in reality, a wolf is present (because the null is false), and you say that we are failing to reject (assume accepting) the idea that there is no wolf. In short, we believe that there is NO wolf, but unfortunately, there is a wolf. We are incorrect here-- we are **** saying that no wolf is present, except he is there (maybe we didn’t see him). This (accepting a false null) would be a Type II error.**

I think failing to reject accepting a false null hypothesis is a Type II error (you got it) which means that I believe there is no wolf present when there is a wolf around (yes)??? which is opposite of my logic above. Your logic here is correct, but above was not.

Related to the t-test, if n increases, I’m more likely to reject a false null hypothesis. Ceteris paribus, yes. Increasing the sample size will increase the power of the test (the probability of rejecting the null when it is false).

If n increases, isn’t my t-stat increasing so it’s more likely to be greater than my t-critical and I accept the null as being true? If your test statistic is beyond the rejection region for the specific test (larger in magnitude than the critical value(s), then you will REJECT the null hypothesis. Larger test statistics imply more statistical significance. Smaller test statistics imply less significance (less likely to reject Ho).

Why is that bad? Accepting a false null (I’m assuming this is what you’re asking) is “bad”, because it consitutes a Type II error, the probability of which is typically unknown, and attempting to quantify it is quite interesting. So, we would rather make Type I errors (if any error), because we can readily control and quantify this probability (assuming your methodology is correct and disciplined-- however, many researchers aren’t so careful).

I hope stats is only 5% of the exam!!!

[lammy]

THANK YOU, THANK YOU. All these negatives -reject, fail, false, null - in one sentence is so confusing!!!

[tickersu]

@lammy

THANK YOU, THANK YOU. All these negatives -reject, fail, false, null - in one sentence is so confusing!!!

Glad to help. All you need to do is break it down into pieces and reassemble it as a clear picture.

[onlysimon]

@Rasec

a type I error (a “false positive”)

perfect. thx!!

[tickersu]

@Rasec

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a “false positive”), while a type II error is the failure to reject accepting a false null hypothesis (a “false negative”)

Fixed that for you

[varunvajpayee]

SImple way to remember:

Type1 Error: Your error term is SMALL (so your denominator will be small hence your t-stats will be large which leads to incorrectly rejecting null hypothesis). Heteroskedaticity and Autocorrelation are suffered from Type 1 error.

Type 2 Error: Your error term is BIG , ( So your denominator will be big hence your t-stats are small, which leads to incorrectly accepting the null hypotheisis). Multicollinearity suffered from Type 2 error.

[tickersu]

@varunvajpayee

SImple way to remember:

Type1 Error: Your error term is SMALL (so your denominator will be small hence your t-stats will be large which leads to incorrectly rejecting null hypothesis). Heteroskedaticity and Autocorrelation are suffered from Type 1 error.

Type 2 Error: Your error term is BIG , ( So your denominator will be big hence your t-stats are small, which leads to incorrectly accepting the null hypotheisis). Multicollinearity suffered from Type 2 error.

“Your error term is small/big” this is incorrect. The error term is the difference between an actual and predicted value for a given observation. The STANDARD ERROR is incorrectly estimated with heteroscedasticity, and the standard error is underestimated with POSITIVE serial correlation.

[varunvajpayee]

I should have mentioned “Standard error” instead of error term.

and positive correlation instead of saying auto correlation. Apart from that above mentioned two statements still hold true.

---

if positive serial correlation is present in the regression, standard linear regression analysis will typically lead us to compute artificially small standard errors for the regression coefficient The citation provided is a guideline. Please check each citation for accuracy before use.These small standard errors will cause the estimated t-statistics to be inflated, suggesting significance where perhaps there is none. The inflated t-statistics may, in turn, lead us to incorrectly reject null hypotheses about population values of the parameters of the regression model more often than we would if the standard errors were correctly estimated. This Type I error could lead to improper investment recommendations

(Institute 190)

Institute, CFA. 2015 CFA Level II Volume 1 Ethical and Professional Standards, Quantitative Methods, and Economics. Wiley Global Finance, 2014-07-14. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.