Lecture 5 Parametric Tests Flashcards
what are the 4 things/points to consider before choosing a statistical test?
- number of groups being compared
- whether the grps are independent or paired/related
- whether the data are continuous, ordinal or nominal
- -> and for continuous data whether the data are normally distributed or not - assumptions underlying a specific statistical test
what is the procedure for hypothesis testing?
step 1: define problem
step 2: state null and alternative hypotheses
step 3: compute test statistic
step 4: find p-value for computed test statistic
step 5: compare p value for computed test statistic w given significance level (usually 0.05)
step 6: state conclusion
(p value < 0.05 –> reject H0; results statistically sig)
(p value > 0.05 –> fail to reject H0; results no statistically sig)
OR
(CI does not include 0 = p < 0.05 or
CI included 0 = p > 0.05)
what is p value:
probability that the observed result or a more extreme result would occur by chance alone, assuming H0 is true
the smaller the p-value, the stronger the evidence against H0
what are the assumptions of paired-samples t test?
- samples are random samples of their populations
- two underlying populations are paired
- the population of differences in values for each pair is normally distributed (have to test for this)
what is the null and alternative hypothesis of paired-samples t-test?
null --> H0 : ud = 0 alternate --> H1: ud /= 0 (2-tailed) or --> H1: ud > 0 (upper-tailed) or H1: ud < 0 (lower-tailed)
what are the 2 examples of paired-samples t-test
- self-pairing (measurements taken on a single subject at 2 distinct points; ‘before’/’after’)
- matching (subjects in one grp matched w those in second grp wrt age, gender etc
how to assess the normality of differences in paired-samples t-test and in independent-samples t-test?
- histogram
- box whiskers
- gold standard: shapiro-wilk (for sample size n <50)
- Kolmogorov-Smirnov test (when n >= 50)
for 3&4:
where H0: distribution of data is normal
H1: distribution of data is not normal
what statistic is used for paired-samples t-test?
- T Statistic
- df = n - 1 (where n = sample size)
- t distribution table is used to find p value
what does a paired-samples t-test test for?
to test the null hypothesis that the mean of the underlying population of differences in values for each pair is zero
(whether there is any difference bet the pairs or not)
what does the independent samples t-test test for?
test the null hypothesis that the two population means corresponding to the two random samples are equal
(whether two groups are equal)
what are the assumptions of independent-samples t-test?
- samples are random samples of their populations
- two underlying pop are independent
- two underlying pop are normally distributed
- two underlying pop have equal variances
(their standard deviation is the same)
(use F or Levene’s test for equality of variances)
–> if variances is not sig different (p >=0.05), use independent samples t-test for equal variances
–> if variances sig (p <0.05), use independent samples t-test for unequal variance
what are the benefits of using levene’s test rather than F test for equality of variances? (independent samples t-test)
F test: assumption = populations from which samples are obtained must be normal
Levene’s test
- -> applicable whether or not data are normally distributed
- -> can be used when >2 groups are being compared
what is F test?
computes the ratio of two sample variances
- if samples have equal variances, ratio of the sample variances will be close to 1
F distribution is usually a family of F distribution (one F distribution for each pair of df), positively skewed and non-negative
what are the H0 and H1, and df for F test?
df1 = n1 - 1 df2 = n2 - 1
H0: no difference in two sample variances
H1: difference in the two sample variances
t statistic for independent sample t-test with equal variances?
df = (n1 -1) + (n2 -1)
t distribution table
