Hypothesis Testing 2

Question 1

What is the correlation test between 2 categorical variables?

Answer 1

Chi-square

Question 2

What is the test for comparing the means for two groups?

Answer 2

T-test for independent samples

Question 3

What are the marginals?

Answer 3

Row and column totals

Question 4

Describe the chi squared test

Answer 4

-Calculate expected variables if independent

Question 5

What is the chi-squared test

Answer 5

The χ
2 value is calculated by comparing the actual
frequencies to the expected frequencies.
• The larger the discrepancy between these two, the less
probable it is that observations like this would occur were
the null hypothesis true.
• More precisely, if the null hypothesis were true, then the χ
2
value would vary according to the χ
2 distribution.
• If the χ
2
is significantly large then we reject the null
hypothesis.

Question 6

How to work out degree of freedom

Answer 6

An r × c contingency table has

(𝑟 − 1) × 𝑐 − 1 degrees of freedom.

Question 7

What happens when there are low frequencies?

Answer 7

The statistics underlying the χ
2
test become inaccurate
when expected frequencies are small.
• Reasons include: inevitable differences up to 0.5 as
observed values can only be whole numbers; and that χ
2
is only an approximation to the exact (but
computationally more expensive) distribution.
• The test is usually considered unreliable for a 2 × 2 table
if any cell has expected value below 5; or for a larger
table, if more than 20% of cells have expected value
below 5.
• For these cases there are more refined methods,
such as Fisher’s Exact Test.

Question 8

What is the T-test?

Answer 8

Purpose: compare the mean of a sample to a
population with a known mean
-Calculate
-We next consult the table of upper critical
values for the t-distribution (e.g. as in this link)
to see if we can reject the null hypothesis
at the significance level of choice.

Question 9

What are the assumptions in the one-sample t-test?

Answer 9

• Normality: the population distribution is
normal
• Independence: the observations in our sample
are generated independently of one another

Question 10

What is the independent samples t-test?

Answer 10

Main idea: compare the means of two samples that
were independently drawn, with the purpose to
determine whether the means of the corresponding
populations are the same
After calculating the t-statistic we consult the
table of critical values for the t-distribution

Question 11

What are the assumptions of the independent samples t-test?

Answer 11

 Normality: the population distribution is normal
 Independence: the observations in our sample are
generated independently of one another, both
within and across samples
 Homogeneity of variance: the population standard
deviation is the same in both groups

Question 12

What are the stages of the chi-squared test?

Answer 12

Chi-square test
 State H0 and H1
 Create contingency table
 Calculate expected frequencies
 Compute χ
2
statistic and consult table of critical
values