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Lecture 1

POLS 3650 Lecture Notes - Lecture 1: Pie Chart, Bar Chart, Statistical Inference


Department
Political Science
Course Code
POLS 3650
Professor
Edward Koning
Lecture
1

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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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