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SYRACUSE / Political Science / PSC 202 / How do we determine if something is nominal, ordinal or interval?

How do we determine if something is nominal, ordinal or interval?

How do we determine if something is nominal, ordinal or interval?

Description

• Key steps in the scientific process  


How do you calculate the standard deviation?



• Formulate research question  

• Remember: an attempt to identify and test empirical generalizations  

• What is wrong with these research questions?  

• Was Obama a good president?  

• Should taxes be increased?  

• Is democracy the best form of government?  

• Propose explanation/theory, hypothesis  

• Explanation/Theory: broad statement about how, and why the world works in a specific  way.  

• Question: Why does some Americans, but not others, think Obama was a good  president?  

• Explanation/Theory: Approval of a president depends on how well voters did  economically during his presidency.  


Why conceptual clarity is essential?



If you want to learn more check out What did mencius teach?

• Hypotheses: Empirically testable statement that follows from a theory.  • Data collection process  

• What kind of data could we collect to test our hypothesis  

• Survey  

• Need information on:  

• Did respondents think Obama was a good president?  

• Income in 2008 and 2016  

• Unemployment between 2008 and 2016, yes or no?  

• Use data to evaluate hypothesis  

• Hypothesis 1: Voters whose income grew between 2008 and 2016 are more likely to  think Obama was a good president  

• True or false?  


What are the types of data collection?



• Hypothesis 2: Voters who lost their job at any point between 2008 and 2016 are less  likely to think that Obama was a good president.  If you want to learn more check out What is structural violence­?

• True or false?

• Reassess explanation  

• Did our explanation/theory find support?  We also discuss several other topics like What are the economic factors that direct developing nations?

• Explanation/theory: Approval of Obama depends on how well voters did economically  during his presidency  

• Yes/no/partly?  

Data Collection Process:

Theory: Independent variable (concept) Dependent Variable (concept)   Example: Religiosity Ideology

Measurement Process:

 Independent variable Dependent Variable  

 (Operationalization) (Operationalization)

 Independent Variable Dependent Variable  

 (measured) (measured)  

Conceptual clarity:  If you want to learn more check out What are the types of noise?

What do we mean by…  

- Religiosity, ideology, democracy, income, etc.  

- Lets take religiosity for example:  

 Measurement Process (operationalization)

 Concept  

 Precise definition of concept (conceptual definition)  

 Measurement Strategy (operational definition)  

 Variable  

 So, the concept of religiosity is defined as the extent to which individuals exhibit the  characteristic of attending religious services.  

• Measurement strategy: How can we measure attendance of religious services?  • A good operational definition provides answers to: What procedure is used to collect data.

Reliability and Validity:

 reliable but not valid (worst) — valid but not reliable (next best) — valid and reliable (best)  

Determining if something is Nominal, ordinal or Interval:  

Say we have two people, A=30, B=60.  

There are 3 things we can say about them:  

- Their ages are different  

- B is higher than A  

- B is two times higher than A (difference)  

 - We cannot measure the difference of things like ideology and gender, (how much more   liberal, how much more of a male)  We also discuss several other topics like What is equality?

Levels of measurement  

Relative  

Difference

Ranking

Exact difference  between units

Nominal

Ordinal

Interval

If you want to learn more check out What are the types of relationships?

Mode

Median

Mean

Nominal

Ordinal

Interval

Examples: Income, Marital Status, support for universal healthcare.  

 Income: Marital Status: Healthcare:  Values: Dollars per year Single, married, divorced Strongly agree, Agree,…  Relative Diff. Yes Yes Yes  Ranking: Yes No Yes  Exact Diff. Yes No No

Mode, median, mean:  

Mode: The number that occurs the most in a data set  

Median: The number in the middle of a number line arranged in numerical order. In a data table,  the median is also the number that corresponds with the first data point after the cumulative  percentage passes 50%  

Mean: The average of all numbers in a data set.  

Finding IQR:  

IQR is the 75th percentile minus the 25th percentile. You find the x value that comes after the  first time the cumulative percent reaches or passes 25% and 75%. You then subtract the number  that goes with the 75%-25%.  

Examples for mean, median, mode and IQR:  

Age Frequency Percent Cumulative 19

17

22.67%

22.67%

20

20

26.67%

49.33%

21

28

37.33%

86.67%

22

7

9.33%

96%

23

2

2.67%

98.67%

24

1

1.33%

100%

Total 75 100%

In this data chart, he mean of the data is 20.47. The median age is 21. This is the first age past  the 50% mark on the cumulative average, and would also be the number in the middle if there  was a number line. The mode is also 21, as more students are 21 than any other age. For IQR,  you find the 75th percentile minus the 25th percentile which in this case is 21-20, giving us an  IQR of 1.

Standard Deviation:  

Given the data from the above chart, finding standard deviation would be…  X x-mean (x-mean)^2 Cumulative Total

19 20 21 22 23 24

-1.47 -0.47 0.53

1.53 2.53 3.53

2.16 0.22 0.28 2.34 6.4

12.46

17 20 28 7

2

1

36.72

4.4

7.84

16.38

12.8

12.46

Sum = 90.6 90.6/6 = 15.1

- Age is the x value.  

- You then take X minus the mean (20.47) for each x value.  - Square the results  

- You add a cumulative column (the frequency)  

Square root of 15.1 = 3.89

- Multiple the (x-mean)^2 by the cumulative number, giving you the total  - Find the sum of the Total (90.6)  

- Divide the sum by the number of x values (6)  

- Then take the square root of that number.  

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