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.
Statistics 

Descriptive statistics 
Inferential statistics 
summarizes (describes) data from a sample using graphs and numbers 
draws a conclusion (an inference) about a population based on data from a sample 
Examples: bar graphs histogram mean and median standard deviation 
Examples: confidence intervals hypothesis tests

Populations and Samples
By collecting information from a representative sample, we can draw conclusions about a population.

Sample:

https://www.omniconvert.com/whatis/samplesize/

Sample statistic:

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
Four levels of measurement 

Qualitative/Categorical can only be grouped 
Quantitative/Numerical can be measured 

Nominal 
Ordinal 
Interval 
Ratio 
Categories with no logical order 
Categories with a logical order 
Zero is arbitrary 
Zero actually means none 
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/samplingmethods/ and http://web.colby.edu/jawieczo/files/2020/01/AmherstTalk_2020_01_24.pdf
Sampling and nonsampling 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 nonsampling.
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.
Errors when using a sample statistic to estimate a population parameter 

Sampling errors 
Nonsampling errors 

cause 
how to reduce 
possible causes 
how to reduce 




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 causeandeffect relationship.
Types of statistical studies 

Observational studies 
Experiments 

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 

Good for: describing populations looking for association between variables 
Good for: establishing causeandeffect relationships 

There are three types of observational studies. 


Survey 
Census 
Case study 

Gathers data from: a sample of a population 
Gathers data from: every individual in a population 
Gathers data from: indepth study of a few individuals 

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.
http://adata.site.wesleyan.edu/schedule/confoundingandmultivariatemodels/
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 doubleblind experiment.
Here is a diagram of a randomized, controlled experiment
https://introductorystats.wordpress.com/2011/03/09/designofexperiments/
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.
Two types of measurement error 

Random error 
Systematic error 
Difference based on chance 
Difference that is consistent 
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. 
High precision: an instrument repeatedly produces the same measurement 
High accuracy: the instrument represents what it purports to measure 
For better precision: take the average of repeated measures 
For better accuracy: improve measurement instrument 
https://www.scribbr.com/methodology/randomvssystematicerror/ 
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.
Measurement errors in statistics 

Difference between the true value and the measured value 
Size of the error relative to true value 
Relative error shown as percentage 
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