Task 3 Flashcards
Define statistical inference
draws conclusions about a population or process from sample data
Name 2 types of statistical inference
- confidence intervals
2. tests of significance
What do the statistical inferences report?
both report probabilities that state what would happen if we used the inference method many times
When you use stat. inference, you assume the data came from what kind of sample or experiment?
random
How do you calculate a confidence interval?
C = estimate +or- margin of error
How do you calculate the margin of error?
z* x σ/square root of n
Define confidence interval
for a parameter is an interval computed from sample data bu a method that has probability C of producing an interval containing the true parameter value
How do you find the area on either side of a confidence interval
1-C/2
Name 2 desirable characteristics of a confidence interval
- high confidence 2. small margin of error
Name 3 ways of reducing the margin of error
- use a lower confidence level
- choose a larger n
- reduce standard deviation
What is the formula for the sample size for desired maring of error?
(z x σ)/m²
Define significance test
a formal procedure for comparing observed data with a hypothesis whose truth we want to address
-> results are expressed in terms of a probability
Differentiate between null and alternative hypothesis
Ho: the statement we want to prove wrong
Ha: the statement we want to prove right
Define statistical significance
the chosen boundary for the p-value, if the p-value becomes equal to or smaller than this number than this number, we reject the Ho, siginificant
aka alpha and usually = 0.05
Define critical value
a value z* with a specified area to its right under the standard normal curve, it is the p-value of exactly 5%
Define power
opposite of type 2 error, the probability of correctly rejecting the incorrect Ho
To increase the power (x3)
- increase alpha (bad solution as type 1 error increases)
- increase n (makes estimator more efficient by decreasing standard error)
- bigger effect (however we cannot control this)
I μtrue - μ I
Define a type 1 error
rejecting Ho when it is true (i.e. accepting Ha)
Deine type 2 error
accepting Ho when it is not true (i.e. rejecting Ha)
What is alpha the probability of?
a type 1 error
How do you calculate a type 2 error using power?
1-p(type 2 error)
If your alpha is too high you increase the probability of a type _ error and decrease the probability of a type _ error
1, 2
What happens to the p-value on 2 sided tests?
you halve the p-value
If zobs is greater than z* the z-score therefore falls into ______
the critical area
How do you calculate the ideal sample size?
n = (z*σ/m)²
m = margin of error
Name one way of reducing the probability of a type 1 error (rejecting a true Ho)
reduce significance level a, however, this is bad for the power as it is then more difficult to reject the Ho
How do you calculate z*?
same as z, just signifies alpha level while not being the p-value of it
What mathematically symbol cannot a Ho not have?
greater than or less to, must have =
Give the z* values for 95%
1.96
When searching for the z* for a confidence level remember ____
you divide the confidence level e.g. 95% -> 5%. Divide by 2 as there are 2 sides, now look for z value
The confidence level pertains to
a) the sample distribution
b) the sampling distribution
b I mean look at the formula, it contains the SE and sure isn’t the confidence interval supposed to show the chances of a population mean lying within it?
How likely are all values in a confidence level?
equal
Power is not applicable ….
in the theoretical situation of a true Ho
A z test can only be performed if the distribution of the population is ____
normal
The p-value assumes that the ____ is true
Ho
What is the critical sample mean?
the sample mean that would lead you to reject the null hypothesis
What does SPSS paired samples correlation tell us?
how well 1 group predicts the scores of another
Why does power increase when df increases?
increasing df means increasing sample size therefore our t* decreases
With df do we round up or down?
be conservative round down!
Why are p-values for t-tests in inequalities and z-tests aren’t?
This is because its a manual calculation, we cannot find exact df in a table however SPSS can
