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POLS 3650 (70)

Edward Koning (60)

Lecture 1

School

University of GuelphDepartment

Political ScienceCourse Code

POLS 3650Professor

Edward KoningLecture

1This

**preview**shows pages 1-3. to view the full**10 pages of the document.**Basic Mathematics

-The upper number in a fraction is called the nominator and the lower is the denominator

-Adding and subtracting = denominator needs to be identical

-Multiplying = multiply both nominator and denominator

-Division = multiply by inverse

-The denominator can never be zero

Order of Operations

-The order of operations determines in which order the calculations in an equation should

proceed (BEDMAS)

Data, variables and attributes

-Data: The information that is subjected to analysis

-Variables: “Categories” of characteristics in our data

-Variables can take on different values and attributes

-Variables may vary from one case to the next

-Attributes: A characteristic of an object or entity

-Statistics: Numerical summary of the data under study

-Are the main tool in quantitative data

-Univariate: Statistics describing only variable (Ex: Average time spent reading news)

-Bivariate: Relationship between two values (Ex: Religious people more likely to appose

same sex marriage)

-Multivariate: Between three or more variables (Ex: Between education, voting and

income)

Sampling and Statistical Inference

-Population: Set of cases we want to make claims about (Ex: Guelph)

-Sample Frame (Study population): Set of cases we draw our sample from (Ex: All landline

numbers in guelph)

-Sample: Set of cases we analyze (Ex: Every 5th number)

-In quantitative data analysis, we should always strive to use probability samples

-Perfect Random Sample: Every case in the population has the same chance of being

selected

-Avoids Selection Bias

-Allows for inferential Statistics: The process of estimating the properties of the

population on the basis of our sample

-Sample Statistics are called point estimates

-Symbols are usually lower-case Latin Letters

-Population statistics are called parameter values

-Symbols are usually Greek letters or upper-case Latin letters

Main Dangers in Statistical Research

Problem 1: Measurement Error

-Measurement Error: Assigning an incorrect value

-Random Measurement error is considered less problematic than systematic

measurement error or measurement bias

-Most important sources of measurement error

-Simple human mistakes

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-Poor Operationalization (process of which we decide to measure the concepts in)

-Always investigate whether the indicators match the concepts that the study draws conclusions

about

-In survey research, ask yourself:

-Would I answer the question in the same way the researchers interpret the answers?

-How is the question worded?

-Do respondents have a reason to give a dishonest answer? (Social desirability bias)

-Are respondents able to answer the question? (Could the answers be non-attitudes)

Problem 2: Sampling Error

Sampling Error: The difference between “true” Population parameters and point estimates of

your indicators

-Any error resulting from your sample

-Every sample necessarily introduces sampling error

-Inferential statistics allows us to estimate this error, but this is impossible to the error is

systematic

-Common sources of sampling bias:

-Non-Probability sampling: Introduces selection bias, volunteer bias

-Sampling frame under represents portion of the population

-In survey research: Low response rate

Problem 3: Incorrect inferences

-Overgeneralization

-Do not generalize beyond your population or study

-Stay as close as possible to your indicators

-Correlation does not equal Causation

-It is tempting to attach causal conclusions to observed associations. But before we

reach this conclusion we need to:

-Give a logical explanation grounded to the theory

-Exclude endogeneity and reverse causality: make sure the DV does not (also

cause the IV

-Exclude spuriousness: make sure that relationship is not caused by a third

variable

Problem 4: Meaningless calculations

-A major danger in statistics - especially in the presence of formidable statistical software

programs - is that we make calculations that do not make sense

-Always ensure that the technique you employ is appropriate

Problem 5: Politics behind statistics

-Politicians, commentators and interest groups know that many people are intimidated by

statistics

-Always ask yourself:

-Does the research have a political interest in the research ﬁnding?

-Do all methodological choices make sense?

-Do the conclusions actually follow from the ﬁndings?

-Are the visualizations fair and accurate?

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Data Preparation

Operationalization

-Identifying unit of analysis, indicators, and possible values (or attributes)

-For quantitative data analysis, all values need to be Coded (I.e. Translated into numbers)

Level of Measurement

-Four possible levels of measurement:

-Level of measurement has a large consequences for the calculations we can

meaningfully conduct

-Nominal: Tells us cases have different values. It categorizes them (Race, Religion)

-Ordinal: A certain rank order that now makes sense (How often you study)

-Interval: In addition to the other two; every step is identical in size (Numbers mean

something)

-Ratio: All previous statements; has a natural zero point (How many aces you get in

tennis)

-Level of measurement is a property of the operationalized indicator, not of the abstract concept

-Higher levels of measurement tend to be preferred because they allow for more opportunities

for data analysis

-It should ﬁrst and foremost make logical sense in light of your research question

Qualitative and Quantitative Variables

-Sometimes nominal variables are called qualitative variables and other variables (ordinal,

interval, ratio) quantitative variables

-It is common to treat ordinal variables as interval/ratio variables if the number of possible

values is large (at any rate higher than 5)

Dichotomous (Binary) Variables

-Dichotomous (binary) variables: A variable that can only assume two values

-Ex: Sex, cat owner

-Dichotomous variables can always be treated as ratio variables as long as their values are 0

and 1

-There is a clear order

-Every step has the same distance

-There is a natural zero point

Continuous vs. Discrete variables

-We can make a further distinction among interval & ratio variables

-Continuous variables can assume any possible non-integer value. More precision is

always possible

-Ex: Age of a basketball player. 25 years > 25 years 6 months > 25 years 6

months 2 days

-Discrete variables can only assume a limited number of (typically only integer) values

-Ex: Number of rebonds of a basketball player in a game

Compiling a data set

-In compiling a data set, we inevitably encounter the problem of missing data (or empty cells)

Two types of missing data:

-User-missing: Respondent gave no answer or no useful answer

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