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research methods and data analysis > chi-squared and t- test > Flashcards

chi-squared and t- test Flashcards

1
Q

what is the chi- square test?

A
  • test of difference among categorical (nominal/ ordinal) variables
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2
Q

what are the two types of chi- squared tests?

A
  • chi- square goodness- of- fit test
  • chi- square test of association
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3
Q

what does the chi- square goodness- of- fit test?

A
  • tests proportions with more than two levels
  • how the proportions in data fit to fixed (expected) proportions
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4
Q

what are binomial tests limited to? how does this differ to chi- square?

A
  • binomial test limited to dichotomous variables (heads/ tails, success/ fail)
  • chi- square test can test more than two categories
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5
Q

what is the null hypothesis of a dice in chi- square goodness of fit test?

A
  • the dice is fair i.e., each face (1-6) has 1/6 probability
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6
Q

what is Benford’s law?

A
  • frequency of first digits of naturally occuring numerical data (prices, populations, lengths, etc) follow a particular proportion
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7
Q

what does chi- square test for Benford’s law test?

A
  • tests whether the frequency of first- digits of the data follow the known proportion
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8
Q

what is the null hypothesis of Benford’s law?

A
  • Benford’s law is persevered
    i.e., numbers are naturally occurring
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9
Q

what happens if the null hypothesis of Benford’s law is rejected?

A
  • it is likely that the data set is fabricated
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10
Q

what is Benford’s law used in?

A
  • various fraud detection scenarios
    e.g., accounting, election, and scientific reports
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11
Q

how do you report results of chi- square goodness- of - fit test?

A
  • explain the experiment
  • X2 value for df (degree of freedom)
  • p value
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12
Q

what does the x2 value show?

A
  • bigger x2= bigger difference
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13
Q

what does the chi- square test of association test?

A
  • compares proportions across two or more groups
  • how proportions of two data sets are associated (test of independence)
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14
Q

what variables does chi- square test of association check association between?

A
  • two nominal/ ordinal variables
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15
Q

how are descriptive tendencies for chi-square test of association summarised?

A
  • summarised into a contingency table
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16
Q

how is chi- square test of association reported?

A
  • reported by chi- square value with df and N (number of samples)
  • followed by p- value
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17
Q

what do the one sample, independent and paired sample t- tests correspond to?

A
  • corresponds to the test for nominal/ ordinal variables
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18
Q

what test does one sample t- test correspond to?

A
  • binomial or chi- square goodness of fit test
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19
Q

what does independent (unpaired) samples t- test correspond to?

A
  • chi- square test of association
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20
Q

what does paired samples t- test correspond to?

A
  • McNemar’s test
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21
Q

what does the one sample t- test compare?

A

-compares the mean of one sample group against a fixed value

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22
Q

what is the null hypothesis of the one sample t-test?

A
  • the population underlying the sample has the mean equal to the fixed value
23
Q

what do the two other t- tests compare? what are they?

A
  • two other t- tests compare a measure across two groups
  • independent and paired
24
Q

what does the independent samples t- test compare?

A
  • the observed differences between the means of two independent samples or categories
25
Q

why is the independent samples t- test called this?

A
  • because the data is from different groups
26
Q

what is the null hypothesis of the independent samples t- test?

A
  • the population underlying the two samples have equal means
27
Q

what are paired samples?

A
  • means the data points are paired across two groups
28
Q

what is the test for paired samples? what is it available for?

A
  • McNamar’s test
  • only available for two dichotomous variables i.e., 2 by 2 contingency table
29
Q

what does the paired sample t- test compare?

A
  • compares the main difference of one group measure on two occasions
30
Q

what is the null hypothesis of the paired sample t-test?

A
  • the population mean did not change
31
Q

what does the student’s t- test compare?

A
  • compare means of populations (three or more means we use a different test)
32
Q

what does student’s t- test show difference in?

A
  • difference in group of measures
    ( interval or ratio variables)
33
Q

what is the null hypothesis of the student’s t- test?

A
  • null hypothesis is that means are equal
34
Q

what is the main assumption of the student’s t-test? what does it mean?

A
  • normality
  • sampling distribution of the mean is normal- if you take groups of n- samples from the distribution and calculate the means of each sample group those means are normally distributed
35
Q

when does the main assumption for student’s t- test hold?

A
  • holds when the sample size n is sufficiently large
36
Q

what is the theorem that describes the main assumption for student’s t- test?

A
  • central limit theorem
37
Q

what are statistical tests based on the normality called?

A
  • parametric tests
38
Q

what should we not always assume in statistical tests?

A
  • shouldn’t assume normality
39
Q

can the normality assumption be checked?

A
  • yes
  • using another stats test
  • test of normality e.g., Shapiro- Wilk test
40
Q

what is violation of the normality indicated by?

A
  • low p- value
    i.e., p < 0.05
41
Q

what other tests are there relating to the assumptions?

A
  • non- parametric tests
  • don’t require the normality assumption
42
Q

what happens when the test of normality fails?

A
  • alternative choices
43
Q

what is the assumption of independent samples t- test?

A
  • equality of variance
  • homogeneity of variance
  • variance of two populations are equal
44
Q

how is the assumption of independent samples t- test tested?

A
  • tested by Levene’s test of equal variance
45
Q

how is the significance of difference in variance reported? what is equal and what isn’t?

A
  • reported as p- value
  • p > 0.05= variance equal
  • p <0.05 = variance not equal
46
Q

what happens if variance isn’t equal?

A
  • theres another test
  • Welch’s t- test
47
Q

what are t- tests based on?

A
  • based on t- statistic
48
Q

what are T- statistics?

A
  • they are like the z- score but about the mean and SD of the sample
  • not the population
49
Q

what does the T- value depend on?

A
  • depends on the degree of freedom
50
Q

how is df worked out?

A

= sample size- number of groups

51
Q

what does a higher t value mean?

A
  • greater difference
52
Q

what is the t- value usually reported with?

A
  • usually with descriptive statistics
  • Mean and standard deviation
53
Q

what does ANOVA compare?

A
  • compares a measure across more than two groups

research methods and data analysis (10 decks)

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