Lecture 5 - effect estimation Flashcards
what is preferably to using p values
emphasis on size and precision rather than p values
what is the aim of a hypothesis test?
provides a frame work to determine the strength of the evidence provided by the data
what is the null hypothesis?(h0)
specifies properties of an assumed population characteristic
what is the alternate hypothesis? (h1)
outlines a contradictory statement from the null hypothesis
when would you use a two-tailed test
testing if calcuated value is above or below what it is expected to be
when would you use a one-tailed test
testing if the calculated value is ONLY below or ONLY above the expected
what is the default position?
assuming the null hypothesis is true
what are the steps in hypothesis testing?
Determining the Two Hypotheses
Computing the Sampling Distribution
Collecting and Summarising the Data(calculating the observed test statistic)
Determining How Unlikely the Test Statistic is if the Null Hypothesis is True (calculating the P-value)
Making a Decision/Conclusion(based on the P-value, is the result statistically significant?)
what is the p-value?
probability of observing data as extreme or more extreme than in a sample, assuming that the null hypothesis is true
what does a small p value suggest?
small p value suggests that the observed data is unlikely to occur if the null hypothesis is true
what will the null hypothesis usually be phrased as ?
no change / no relationship / no difference
what will the alternate hypothesis usually be phrased as ?
change present / there is a relationship / there is a difference
when would you reject the null hypothesis
p value < 0.05 and conclude that a statistically significant relationship exists
what is the significance level?
cut off for the p-value
what is a type I decision error?
occurs we reject the null hypothesis but infact the null is true
- the probability of this occuring is equal to the cut off for the p value
what is a type II decision error?
rejecting the alternate hypothesis when the alternate hypothesis is true
denoted by beta
what does the chance of an error depend on?
sample size
magnitude of true relationship
cut off for the p-value
what is the power of a test?
probability that the sample we collect will lead us to reject the null hypothesis when the alternative hypothesis is true
probability of not making a type II error –> 1-B
what is the recommended power and how can it be increased?
80-90%
increased by increasing the sample size
what should be considered alongside the p-value
size (strength)
precision ( confidence intervals )
quality of research design
confounding variables
what does the chi-squared statistic measure?
magnitude of the difference between the sample observations and the calculated expectations
what do chi-squared values suggest
If expectations in the population are the same, then the Chi-squared tends to be small (near 0)
If expectations in the population are different, then the Chi-squared tends to be large
what is the critical value for 2x2 table?
3.84
a value greater than this suggests a statistically significant relationship
when is the fisher’s exact test applied?
if there are any expected values <5
more conservative
what does the Chi-squared statistic show?
whether or not there is a statistical relationship between two categorical variables
what does the chi-squared statistic not tell you?
the direction of association
RR / OR can identify this
why are 95% CI more informative than a test of significance ?
they stipulate the level of precision of the sample estimate of the RR
what are two key conclusions regarding the 95% CI of the RR
if it includes 1 it is not statistically significant
if it excludes 1 it is statistically significant
what is the mcnemars test
Chi-squared test for matched samples
- measurement of the same individuals at different time points
- chi squared would ignore the correlation between individuals
what are the t/z test used for?
continuous data
what is h0 and h1 for a single mean?
h0 = population mean equals a certain value h1= population mean does not equal a certain value
what test can you apply with > 30 observations
z test
no assumptions
what test can you apply < 30 observations and what are the assumptions
t-test
sample was selected randomly
must be taken from a normally distributed population
what happens when you have an independent sample for two means in terms of the hypothesis?
h0= population mean in sample 1 will equal the sample of 2
