Hypothesis Testing with Ordinal and Nominal Variables: Chi-Square Statistic and T-Test, Lecture notes of Social Statistics and Data Analysis

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Hypothesis-testing with Ordinal/ Nominal

Variables:

• Use (t-test) when one variable is measured

at the interval/ratio level , and the other

variable involves 2 groups. However, when

testing a hypothesis with two variables

measured at the nominal or ordinal level you

should use the chi-square statistic.

• With nominal measurement we categorizes

a variable; at the ordinal level we have

enough information to rank-order a variable

in terms of greater of less than.

Ordinal measurement:

What is your annual gross income?

**_1. less than $10,

2. $10,000 to $19,
3. $20,000 to $34,
4. $35,000 to $59,
5. $60,000 to $89,
6. $90,000 or more_**

Nominal measurement:

Your religious affiliation is…

**_1. Protestant

2. Catholic
3. Other religion_**

OBSERVED FREQUENCIES (Actual data)

• Statistical tests tell us when observed data

differ so much from what we would expect

by chance, that we can conclude that a real

difference exists. Hypothesis testing

assesses differences between what we

expect if the null hypothesis is true, and

what is in our data …. the t-ratio does this for

means & proportions; chi-square for

frequency counts.

• Chi-square tells us if observed

frequencies differ so much from what

we would expect from chance that we

can reject the null hypothesis.

OBSERVED FREQUENCIES (Actual data)

• A
• B
• C
• D
• E
• A EXPECTED FREQUENCIES (If Null Hypthosis is true)
• B
• C
• D
• E
• A
• B
• C
• D
• E
• A EXPECTED FREQUENCIES (If Null Hypthosis is true)
• B
• C
• D
• E

• The null hypothesis is there are no sex

differences (or at least no difference big

enough to rule out chance) in the reasons

students give for attending university.

• The research hypothesis is there are sex

differences in the reasons students give for

attending university.

• If the difference between observed and

expected frequencies is so large that it is

unlikely due to chance, we reject the null

hypothesis.,