chi-squared and t-tests (w6) Flashcards
what test to use when proportions with more than 2 levels
chi-squared goodness of fit test
what test to use when comparing proportions across 2 or more groups
chi squared test of association
what test to use when comparing a measure with a fixed value
one sample t test
what test to use when comparing a measure across 2 groups ( independent and paired )
independent: two samples t test
paired: paired t test
what test to use when comparing measure across more than two groups
ANOVA
what is chi squared a test of
test of difference among categorical (nominal and ordinal) variables
what are two types pf chi squared test
goodness of fit
test of association (or test of independence)
what is chi squared goodness of fit test for
how proportions in data fit to fixed (expected) proportions
what is chi squared test of association for
how proportions of two data sets are associated
what is Benford’s law, aka
first digit law
the frequency of first digits of naturally occurring numerical data follow a particular proportion (eg prices, populations, lengths)
what does the chi squared test for Benford’s law test
whether the frequencies of first-digits of the data follow the known proportion
what is null for testing Benford’s law, what does it mean if its rejected
Benford’s law is preserved (i.e. numbers are naturally occurring)
data set is likely fabricated
how to report chi squared goodness of fit test
the X2 value for df followed by p-value
eg: X2 (5) = 12.2, p=0.032
in chi squared goodness of fit test, what does bigger X2 mean
bigger difference
what can descriptive statistics for chi squared test of association be summarised as
contingency table
how to report chi squared test of association results
X2 value with df and N (number of samples) followed by p-value
eg: X2 (2, N=27) = 1.43, p = 0.490
what’s a paired sample
means data points are paired across 2 groups
eg is variables are mom L or R handed and daughter is L or R handed, mom-daughter data need to be paired
when can McNemar’s test be used
only for 2 dichotomous variables (ie 2-by-2 contingency table)
what is t test for, what variables
difference in group of measures (interval or ratio variables), compare means of populations (3 or more means use a different test)
what is null hypothesis for t test
that means are equal
what are three types of t test
one sample
independent (unpaired) samples
paired samples
what you can decide for each t test
whether to do a one-tailed or two-tailed test
what test for nominal/ordinal variables the one sample t test corresponds to
binomial or chi squared goodness of fit
what test for nominal/ordinal variables the independent (unpaired) samples t test corresponds to
chi squared test of association
what test for nominal/ordinal variables the paired samples t test corresponds to
McNemar’s test
whats the one sample t test for
compares mean of one sample group against a fixed value
what is independent samples t test for, why is data called independent
compare the observed difference between the means of two independent samples or categories
data is from different groups
what is paired samples t test for
compare the main difference of one group measure on two occasions
what does normality assumption for t test mean, what is this called
sampling distribution of the mean is normal
central limit theorem
what are statistical tests based on normality assumption called
parametric tests
how to check normality assumption, what indicates violation of normality
test of normality (shapiro-wilk test)
low p value (p<0.05)
what’s an assumption for independent samples t test
equality of variance: variance of 2 populations are equal
how to test equality of variance, what is p value in this context
Levene’s test of equal variance,
significance of difference in variances are reported as p value
how to know if variance is/isn’t equal, what to do if variances aren’t equal
p < 0.05 : variance not equal
p > 0.05 : variance are equal
use Welch’s test
how to write result for one sample t test
eg: UoB students reported higher levels of stress (M = 62, SD = 4) than found in the population of the same age group,
t(36) = 2.4, p = .034
how to write result for independent samples t test
There was no significant effect of gender on the exam score, t(138) = 3.7, p =.097, despite women (M = 65, SD = 8) attaining higher scores than men (M = 61, SD = 6.8)
how to write results for paired samples t test
The results from the pre-test (M = 12.1, SD =1.4) and post-test (M = 14.1, SD = 1.7) memory task indicate that energy drink have significantly improve the memory, t(19) = 3.1, p = .006
what does t value depend on
df = sample size - no. groups
what does greater t value mean
greater difference, usually reported with M and SD
when to use one sample t test
one group, normality
when to use Wilcoxon signed ranks test/one-sample median
one group, no normality
when to use independent samples t test
two groups, unpaired, normality, equal variance
when to use Welch’s test
two groups, unpaired, normality, no equal variance
when to use Mann-Whitney U test
two groups, unpaired, no normality
when to use paired samples t test
two groups, paired, normality
when to use Wilcoxon signed ranks test
two groups, paired, no normality
