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SOC411 - Quantitative data analysisJanuary 16
We study social statistics to have a bigger scope than other kinds of research, generate your own statistics, evaluate the
statistical arguments that others use, and it will get you a job.
Sociologists do exploratory, explanatory, and predictive research, often to support social change.
The three main areas of difference between quantitative and qualitative research are sampling, collecting data, and analyzing
data.
Statistics are inherently political, they started as the subject of the state because they are used to support and motivate
policies and social processes.
Statistical analysis relies on the process of quantification, translating a concept, idea, behavior, or other into numbers;
analyzing them, and then retranslating.
Quantification can happen in different questions:
- Turning the opinion into a number (What do you … from 1 to 10)
- Strongly disagree to disagree, the researcher assigns to each answer a number
- Other
Variable Province the opposite is a constant
Attributes Ontario, Quebec
Values 35, 45 Numbers can be a number coming from the answer of the people, or they can be the
product of the quantification of the researcher
Recoding a variable means changing the values assigned to each attribute
Sample size, variables required, numerical summary tools, and conclusions are the four elements of a descriptive statistics
problem.
,January 23
Levels of measurements: the attributes of a variable determine its level of measurement. We divide attributes into categories
(provinces) or quantities (How much do you agree with this from strongly agree to strongly disagree? how long does it take for
you to commute to class?). Categorical variables are either nominal-level (the order doesn’t matter – dichotomous variables
are variables with only two attributes [yes/no]) or ordinal-level (the order of answers matters – strongly agree, agree, etc.);
the attributes are categories. Count variables are when the attributes are numbers, and ratio-level is when the quantity
divided by 2 or doubled makes sense – the value corresponds to the quantity of the attribute.
There are usually two totals: total and valid total.
Be careful of class intervals: when the attributes of a variable are ranges of quantities and not single quantities. In this case,
the variable has an ordinal level. They can’t be ratios because it doesn’t make sense when you divide them in half or double it.
Social statisticians use descriptive statistics (to summarize information) and inferential statistics (to make estimates or
predictions of a population from a sample of it)
Stats analysis can include different numbers of variables: univariate analysis (1 variable), Bivariate analysis (2), multivariate
analysis (more)
Frequency tables: frequency distribution or frequency tables are the most basic summary technique. They show how
frequently each attribute occurs. They include:
Raw counts (frequencies)
Percentages (valid percentages don’t count the missing answers, cumulative percentage adds up everything that
comes before)
Cumulative percentage
Missing values usually include attributes that aren’t useful information
A graph has to include a title with the number of cases (n), percentages (no frequencies of counts), axis titles, labels, and a
legend.
The independent variable is the one that creates the outcome on the dependent variables (A researcher is studying the
relationship between education and poverty to see if education level affects an individual's income level. education is
independent and because we are trying to see its output in income which is depending on education)
Data synthesis is the process of taking raw data and organizing it into a format that is easy to understand and analyze
A continuous variable is a variable whose value is obtained by measuring, i.e., one which can take on an uncountable set of
values. The opposite is a discrete variable.
The unit of analysis is the entity that frames what is being looked at in a study or is the entity being studied.
, January 30
How to describe the center of a categorical variable (variables that have attributes as categories [nominal, dichotomous, and
ordinal level])
In addition to frequency tables and graphs, we can also summarize the distribution of variables using various statistics.
Depending on the variable’s level of measurement, these include stats that describe the center, spread, and shape of the
distribution of a variable
For nominal-level variables, you can only report the center of a variable using the mode, for an ordinal level you can do mode
and median, and for the ratio, you can do mode, median, and mean.
- Mode: the attribute/value that occurs most frequently. Ignore missing values. Ascending/descending counts on
frequency tables may only be used for nominal-level variables.
- Median: the middlemost point of distribution. To find it you can put the cases in order from the lowers
attribute/value to the highest and find the case that is in the middle position (total number of cases + 1)/2. You can
also find it using the cumulative percentage looking at where it goes over 50%. - this gives you the POSITION of the
percentile in the list
the median can be between two positions if the list is made of an even number of cases
- Mean: average value of the distribution
For categorical level variables we report the category or the attribute and not the value.
Describing the dispersion/spread of ordinal variables. Nominal level variables don’t have any way to do this. For ordinal level
variables, you can use:
- Range: the distance between the lowest and the highest attribute in the distribution. This can be found by putting the
cases in order and finding the highest and lowest position (it’s meaningless to report the distance, we usually report
min and max)
- Interquartile range (IQR): the distance between the 25th percentile, and the 75th percentile of the distribution. It tells
us about the spread of the middle 50% of the cases excluding extreme cases. You can find it by looking when the
cumulative %: when it goes over 25% and 75%. Another way is (number of cases + 1) x 25% and (number of cases + 1)
x 75% - this gives you the POSITION of the percentile in the list
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