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Hypotheses are assumptions about ___
population parameters NOT sample statistics (ex. studying 10 hours leads to better results than studying only 5 hours)
what are the steps for hypothesis testing (NHST)?
set up a hypothesis (H0 and H1)
choose alpha level, aka the cutoff value/critical value (0.05 unless told otherwise)
examine data and decide which statistical test to use (z,t,f)→ know when these are used
make a decision whether to reject or not reject the null hypothesis (i.e. whether the result is significant enough)
what does the p-value represent?
the probability of finding an effect in the observed statistic under the assumption that the null hypothesis is true
if p is less than or equal to a, reject the null
a statistically significant effect does not mean that…
we have a precise estimate of the effect (errors, effect of pop maybe smaller or larger than estimate, standard error of estimate)
the effect is important or meaningful (depending on the scale—the cutoff, it helps us determine whether there is a significant effect given our dataset)
what does a confidence interval give us information about?
the precision of our estimates
a CI should contain the population parameter but this doesn’t mean it always will
How does sample size influence the precisions of our estimates?
larger sample= more precise
smaller sample= less precise
CI beocmes more narrow =more precise
What happens to the CI as alpha decreases?
the CI becomes larger or wider (less precise)
What are some commonly used effect size measure in NHST?
pearson’s correlation r or r squared
cohen’s d
omega or omega squared
eta squared
what are considered small, medium and large effect sizes?
small: r=0.10, r² = 0.01, d= 0.2
medium: r=0.30, r²=0.09, d= 0.5
large: r= 0.50, r²= 0.25, d= 0.8
what are the two types of errors in hypothesis testing and define them
type 1 error (a): rejecting null hyp when it is true (false positive)
type 2 error (beta): retaining null hyp when it is false (false negative)
what is power (1-beta)
The probability of correctly rejecting a false H0
what is the relationship between alpha and beta?
Higher values of alpha (type 1 error) means lower values of beta (type 2 error), which means the power to reject the null is higher
the two are inversely related
what information do you need to compute a z-test
know population standard deviation and sample size??
what is the purpose of a single mean z-test?
test whether the population mean is equal to some hypothesized value based on the sample mean that we have
what are the assumptions of a single mean z-test?
normal distribution
sample is simple and random (independence of observations)
the population standard deviation must be known
z score for sample score formula
z=x-μ/σ
what is the formula for z-statistic for sample mean?
z= x̄- μ0/σx̄
σx̄ : sample standard deviation (i.e. standard error)
σx̄= σ/√N
μ0= test value
what are the limitations of the z-test?
knowing the true population standard deviation is unrealistic (unless the entire population is known)
this is why t-tests are alternatives to z-tests
what is the purpose of a t-test?
to test whether the population mean is equal to some hypothesized value based on the sample mean
** we have no information about the population standard deviation
what are the assumptions/ requirements of t-tests?
the variable is normally distributed
the sample is simple and random (independence of observations—in no way influenced by measurements of other subjects)
what is the formula t-test statistic?
t= x̄- μ0/sx̄
μ0: hypothesized population mean (i.e. 0)
x̄: sample mean
sx̄= s/sqrt N (standard error)
who was the t distribution discovered by?
William S. Gosset in 1908 (a.k.a “student’s t distribution)
How does the t distribution vary in shape?
the shape varies according to the degrees of freedom (N-1)
+ sample size= +df
distributions are quite close to the normal distribution for df>30
as N +, t approaches z
Note 
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