NHST Overview, Type 1 and Type 2 error Flashcards
What is a type 1 error?
When H0 is true but you reject it
When H0 is true but you reject it
What error type is this?
Type 1
What is type 2 error?
When H0 is false but you fail to reject it (you don’t reject it)
When H0 is false but you fail to reject it (you don’t reject it)
What error type is this?
Type 2
What causes a type 1 error?
Random sampling error
What causes a type 2 error?
Methodology errors
Why do type 1 errors occur?
Because even if your p-value is small there is still a (small) chance that your data were unusually extreme (and so you rejected the
NULL) just due to sampling error
Why do type 2 errors occur?
Because of (most likely) problems in the study
e.g.
- Perhaps your sample was biased
- Perhaps there was an error in your experimental task
- Perhaps your sample size was too small
Why do we use 0.05 as the “cut-off” for the probability of an event happening?
Because 0.05 is small enough that it makes it difficult for us to reject the hypothesis but it is also not too extremely small that it’s impossible to reject the hypothesis
You conduct a z-test and find that z = 1.75, p = 0.0401. You reject the null hypothesis in favour of the reseach hypothesis. In reality the research hypothesis is actually incorrect.
True or false - you made an error in rejecting the null hypothesis and should have failed to reject
a. True
b. False
b. False
You did the right thing - you rejected H0 which was incorrect
You conduct a z-test and find that z = 1.75, p = 0.0401. You reject the null hypothesis in favour of the reseach hypothesis. In reality the research hypothesis is actually incorrect.
True or false - you made a type 2 error?
a. True
b. False
b. False
It’s a type 1 error because if H1 is incorrect, then H0 is correct but you’re rejected it
You plan to conduct a z-test with an alpha value of 0.05 (5%). Before you conduct your experiment the probability of making a Type 2 error is 5%.
a. True
b. False
b. False
Fill in the blank
You conduct a z-test with an alpha value of 0.05 (5%). You find that z = 1.75 and p = 0.0401. Before you conducted your experiment the probability that you would make a (…….) error was (…….)%
- Type 1
- 5%
Because 0.04 is so close to 0.05 and you might’ve had some extreme values in your results so you end up rejecting H0 because p<0.04
You conduct a z-test (with α = 0.05) to investigate whether the earth’s gravity (which is higher than that on Ziltoidia 10) means that visiting aliens from Ziltoidia 10 are shorter on earth than back home. You know that height on Ziltoidia 10 follows a normal distribution: N(25, 2.5). Your 1-tailed research hypothesis states that Ziltoidians on earth are shorter than on Ziltoidia 10. To test this hypothesis you gather a sample of 25 Ziltoidians and measure their heights. The sample mean is 24cm.
By carrying out z-test, calculate the value of z and p and based on these values decide whether to reject the null hypothesis. Which of the following is the most appropriate summary of your findings?
a. z = -2.0, p = 0.9772 Since p > 0.05 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10 b. z = -2.0, p = 0.0228 Since p < 0.05 we can reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10. There is evidence that Ziltoidians are shorter on earth. c. z = -0.4, p = 0.3446 Since p > 0.05 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10 d. z = -0.4, p = 0.6554 Since p > 0.05 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 1
s.e. = pop. SD / SQRT (sample size)
s.e. = 2.5 / SQRT (25)
s.e. = 0.5
z score = (x - mean) / e.s.e.
z score = (24 - 25) / 0.5
z score = -2.00
p value = 0.0228
p < 0.05, reject H0
Answer = B
You conduct a z-test (with α = 0.001) to investigate whether the earth’s gravity (which is higher than that on Ziltoidia 10) means that visiting aliens from Ziltoidia 10 are shorter on earth than back home. You know that height on Ziltoidia 10 follows a normal distribution: N(25, 2.5). Your 1-tailed research hypothesis states that Ziltoidians on earth are shorter than on Ziltoidia 10. To test this hypothesis you gather a sample of 25 Ziltoidians and measure their heights. The sample mean is 23.5cm.
By carrying out z-test, calculate the value of z and p and based on these values decide whether to reject the null hypothesis. Which of the following is the most appropriate summary of your findings?
a. z = -3.0, p = 0.0013 Since p < 0.05 we can reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10. There is evidence that Ziltoidians are shorter on earth. b. z = -3.0, p = 0.0013 Since p > 0.001 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10. c. z = -0.6, p = 0.2743 Since p > 0.05 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10. d. z = -0.6, p = 0.2743 Since p > 0.001 we can not reject the null hypothesis stating that there is no difference between Ziltoidian height on earth vs. Ziltoidia 10.
s.e. = pop. SD / SQRT (sample size)
s.e. = 2.5 / SQRT (25)
s.e. = 0.5
z score = (x - mean) / e.s.e.
z score = (23.5 - 25) / 0.5
z score = -3.00
p value = 0.0013
p > 0.001, fail to reject H0
Answer = B
