This video gives an introduction to some of the basic ideas you need to get started.
Descriptive and Inferential Statistics
There are two major fields in statistics. QM starts with descriptive statistics then moves to inferential statistics.
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Statistics |
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Descriptive statistics |
Inferential statistics |
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summarizes (describes) data from a sample using graphs and numbers |
draws a conclusion (an inference) about a population based on data from a sample |
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Examples: bar graphs histogram mean and median standard deviation |
Examples: confidence intervals hypothesis tests
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Populations and Samples
By collecting information from a representative sample, we can draw conclusions about a population.
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Sample:
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https://www.omniconvert.com/what-is/sample-size/
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Sample statistic:
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Variables, Types of Data, and Levels of Measurement
A variable’s level of measurement determines the type of graphs, measures of center and spread, and statistical tests that can be conducted.
An easy way to remember the levels of measurement is using the acronym N.O.I.R
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Four levels of measurement |
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Qualitative/Categorical can only be grouped |
Quantitative/Numerical can be measured |
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Nominal |
Ordinal |
Interval |
Ratio |
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Categories with no logical order |
Categories with a logical order |
Zero is arbitrary |
Zero actually means none |
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marital status hair color gender blood type |
level of satisfaction (very low to very high)
education level (secondary to PhD) |
temperature (F° or C°) SAT scores dates grade point average |
age height income cost of data plan |
Reliable data comes from a sample of individuals that accurately represents the population of interest.
Biased sampling methods (like convenience sampling or voluntary response sampling) may not produce a representative sample because some part of the population may be underrepresented or overrepresented.
To get unbiased samples, we choose a random sampling method, based on probability, that gives a representative, unbiased sample.
In this video we will be looking at the different methods of obtaining a sample.
adapted from: https://www.scribbr.com/methodology/sampling-methods/ and http://web.colby.edu/jawieczo/files/2020/01/AmherstTalk_2020_01_24.pdf
Sampling and non-sampling error
A sample statistic will never be a perfect representation of the population parameter—it is always an estimate.
There are two types of errors of possible errors: sampling and non-sampling.
We can measure sampling error by using the margin of error, or, how many points your sample statistic may differ from the true population parameter.
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Errors when using a sample statistic to estimate a population parameter |
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Sampling errors |
Non-sampling errors |
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cause |
how to reduce |
possible causes |
how to reduce |
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This video summarizes why we use a probability sample and take a large sample to reduce sampling error.
Experiments and observational studies are the main two types of statistical studies that social science researchers use.
In observational studies, we record the traits of individuals—we do not want to change their beliefs or behaviors. We want to describe a group or explore relationships between variables.
In experiments, we deliberately change a variable to see how it impacts other variables. We want to establish a cause-and-effect relationship.
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Types of statistical studies |
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Observational studies |
Experiments |
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Researcher: records characteristics of individuals with no intention of changing their beliefs or behaviors |
Researcher: intentionally manipulates one variable (the treatment) to see how it affects other variables |
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Good for: describing populations looking for association between variables |
Good for: establishing cause-and-effect relationships |
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There are three types of observational studies. |
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Survey |
Census |
Case study |
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Gathers data from: a sample of a population |
Gathers data from: every individual in a population |
Gathers data from: in-depth study of a few individuals |
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This video summarizes the main differences between an observational study and an experiment.
Experiments
The objective of an experiment is to determine if the change in one variable (explanatory variable) causes change in another variable (response variable). This explanatory variable is called the treatment.
All other factors must be controlled so we know that the it is only the explanatory variable that is causing the change in the response variable. So, we must eliminate any confounding, or lurking, variables that might also impact the response variable.
The placebo effect is another factor that can limit the effectiveness of a study. The placebo effect is when individuals believe that there they have experienced a change because they expected it by virtue of participating in the study.
To reduce the impact of confounding variables and the placebo effect, researchers do two things:
In this video we will be talking about placebo effect, control groups and double-blind experiment.
Here is a diagram of a randomized, controlled experiment
https://introductorystats.wordpress.com/2011/03/09/design-of-experiments/
An experiment is considered to be the “gold standard” in research, but many social research questions can only be answered using an observational study. How do you decide?
Measurement error is the difference between the observed (measured) value and the true value.
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Two types of measurement error |
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Random error |
Systematic error |
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Difference based on chance |
Difference that is consistent |
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The measurement fluctuates: sometimes it’s higher than the true value and sometimes it’s lower. |
The measurement is always higher or lower than the true value. |
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High precision: an instrument repeatedly produces the same measurement |
High accuracy: the instrument represents what it purports to measure |
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For better precision: take the average of repeated measures |
For better accuracy: improve measurement instrument |
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https://www.scribbr.com/methodology/random-vs-systematic-error/ |
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This video gives a clear example of the difference between accuracy and precision.
Other measurement errors in statistics
It’s important to recognize the types of measurement errors.
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Measurement errors in statistics |
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Difference between the true value and the measured value |
Size of the error relative to true value |
Relative error shown as percentage |
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True value - measured value |
Absolute error True value |
Relative error x 100 |
This video shows how to calculate absolute change and relative change using percentages.
Statistics Canada also has a useful guide to using percentages in statistics.
For tips on how to decide if a study is trustworthy, have a look at this webpage, Factors to Consider When Evaluating Statistics
For example:
Collection Methods & Completeness
