Task 4 Flashcards
Discuss one sample t-test vs paired sample t-test
- > computationally the same (see formula)
- > paired is just one sample t test but performed on a set of difference scores (d)
Is the independent t-test computationally the same as one sample and paired sample?
no
How to create a confidence interval for a one sample t-test?
same as z test just replace z* with t*
p-values are only exact when the distribution is
normal
p-values are normally distributed when
the Ho is true
Why is it important to use the right distribution?
The whole point of using the correct distribution (normal, t, f, chisq, etc.) is to transform from the test statistic to a uniform p-value. If the null hypothesis is false then the distribution of the p-value will (hopefully) be more weighted towards 0.
What does the usefulness of t-tests depend on?
results of a one-sample t-test are exactly correct only when population = exactly normal which real populations never are, therefore usefulness of t procedures depends on how strongly they are affected by non-normality (robust - not strongly affected)
What are t-procedures
a) robust against
b) not robust against
a) robust against non-normality of the population except in case of outliers or strong skewness
b) not robust against outliers because sample mean x and sample standard deviation are not resistant to outliers
How can you improve the p-value accuracy and critical value accuracy from t distributions when population is not normal
large n
How to increase confidence level?
increase z*
What is pooled standard deviation? (Sp)
combination of sample standard deviations, used when equal variances assumed
What is Levenes test?
tests if Ho: variance of samples equal
if largest s/smallest s is less than 2, we assume equal variances therefore use pooled independent samples t test
What distribution is required to conduct a one samples t-test?
sample must be drawn from a normally distributed population
- > if population is normal, sampling distribution will be normal
- > make sure sample is large enough if violated, the sampling distribution will then become approx normal due to CLT
How do we know whether to conduct a z-test or t-test?
for z-test the population stnadard deviation is known
for t-test the population standard deviation is not known therefore we use a sample standard deviation
How many random variables are involved in a t-test?
How does this affect the distribution?
2, the sample standard deviation and sample mean as these vary among different samples
-> distribution becomes more dispersed
How can you improve the efficiency (accuracy) of a sample standard deviation (which is an estimate) for t-tests?
large n, will resemble more and more as an average deviation causing dispersion to decrease approaching almost a normal z-distribution
Which is less reliable and powerful, z-test or t-test and why?
t-test is less powerful as the distribution is broader (standard deviation used is an estimate)
What does a t-test assume about the variable in the study and what to do if violated?
assumes its quantiative e.g. number of socks
-> if violated then use X^2 goodness of fit
Why do we use degrees of freedom?
to make up for lowered reliability (bigger the sample, more reliable)
Since all t-values are positive, what do you do if you get a negative one?
just search the same number but positive, the p-values are the same as the t-distribution is symmetric
How do you calculate the degrees of freedom for
a) one sample t test
b) paired samples t test
c) independet samples t test (variances assumed and unassumed)
a) n-1
b) n-1
c) assumed -> n1+n2-2
unassumed -> (lowest ni)-1
Both samples in a paired samples t-test are…
a) independent or
b) dependent
b
Paired samples t-test is a
a) within subjects design or
b) between subjects design
why?
within subjects design
- > repeated measures of the same person
- > pairs of people matched
What is the difference between paired samples t-test and independent samples t-test
in paired samples they are dependent hence a within subjects design (repeated measures of the same person, pairs of people matched)
in independent samples they are independent hence between subjects
What is correlation like in paired samples t tests?
high
When is a t-statistic
a) normally distributed
b) has a t distribution
a) when n is greater than 25 -> use z table
b) when n is less than 25 -> use t table
Why don’t we have equal variances in paired but in independent?
paired is to measure differences so we need variation therefore assume unequal variation
How to find t*?
you need the df and p-value, then given in t-table
In a paired samples t-test, what kind of variable are subjects paired on?
a within-subjects variable e.g. IQ
gender, for example, is a between-subjects variable
Differentiate between a within-subjects and between-subjects variable
-> when do we use each one?
Within-subjects variable: an independent variable that is manipulated by testing each subject at each level of the variable.
-> paired t-tests
Between-subjects variable: different groups of subjects are used for each level of the variable.
-> independent samples t-test
What marks the threshold?
x-bar *
