Quick Description
Statistics is an area of mathematics, an everyday tool and a collection of formulas. Formulas and calculations are what most people think of when asked about statistics. But thinking is the most important component. It all starts with thinking.
I used to be a statistics consultant. People pay me money to evaluate their projects or processes. The worst was when doctoral students would come with their data in hand and ask me what it means. They were very motivated to complete their dissertations and only needed with one little thing: the analysis. I wanted to scream.
Statistics is something you tag onto the end of the process. It is part of the project. They could tell me who they tested but had trouble explaining why those people, why those questions, and what they expected to find. These are all part of statistics.
I couldn’t scream, so I raised my prices.
Quick Tour
Let me give you a quick tour of statistics. At its cote statistics starts with thinking. It can be taught as a series of calculating procedures but that is an unfortunate oversimplification. Just as music includes physics, mechanics and mathematics, statistics includes planning, collecting, organizing, analyzing, integrating and presenting data. It is a complex process. There are 10 things to keep in mind concerning statistics. They are each interesting alone but they combine to give a much fuller picture of the process.
Measurement. Before you ask people questions, observe rats running down mazes, or see how people act when in a group, there are 5 questions you need to ask yourself.
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- What are you trying to prove?
- What is it like in practice?
- Who is predicting whom?
- Who are you going to study?
- What do the numbers mean?
Central Tendency. The challenge is to find a single number to represent a group. We could use an ID number to indicate which group but it wouldn’t tell us much about the group. We could use the number of people in the group but that too is un informative.
Fortunately, the universe has predictable patterns. There are movements of stats, orbits of planets, and the speed of light. And there is the pattern of chance. We recognize non-chance patterns when we see them: neat rows and columns, toys put away in the cupboard, and clothes hung in the closet.
We recognize chance patterns when we see heaps, mounds and piles. If you dump out a bucket of toys and the all arrange themselves by height, something is wrong. That’s not what chance looks like. A heap or mountain of scores is what chance looks like. And if we measure enough people every variable follows this pattern. As with all mountains, we look for the peak in the middle of the mountain.
Dispersion. If central tendency looks for the middle of the group, dispersion tries to evaluate commonality. When a measure of dispersion is large, the width of the distribution is wide and the score vary greatly. A small amount of dispersion means there is less variability in the scores. Dispersion measure include range, Sum of Squares, variance and standard deviation.
Z Scores. Real data is bumpy and ragged. To smooth it out into a theoretically perfect curve, we use Z scores. Each raw score is converted into z’ s, and the mean and standard deviation are set to whatever values you want. Z scores, in a simpler chase, can be used to identify the location of any score in terms of standard deviations. It is easier than it sounds.
Correlation. The long way first: two observations are taken on each person in the study. Both scores are converted into their respective z scores. The z scores are multiplied together. Repeat for all pairs. Take the average of the products. If positive, it is a positive correlation. This demonstrates the correlation is a product moment measure. The short way: throw the raw scores into a formula and be done with it.
Statistics often has a long way which demonstrates the underlying logic, and a short way people actually use.
Regression. In research, we are always check to see if our data looks like one model or another. In central tendency, we are checking to see if it looks like a symmetrical mountain. In a regression, we are checking if scatter plot looks like a straight line.
Probably. All about likelihood and chance.
Independent t-Test. Comparing two means to see if they are significantly different. Only one independent variable but high-low comparisons.
One-Way ANOVA. Big brother of the t-test. Compare the means of 3 or more means without worrying about some will look significant by chance. Only one independent variable but high, medium and low comparisons.
Advanced Procedures. Procedure that have mor than one independent variables.
How To Calculate Statistics
All you need to calculate common statistics, all in one place.
In real life, computers do the calculating. it is a great way to work with large data sets. Students can get a feel for what the work is like. And they can spend more time interpreting the results than doing data entry.
But there is value is doing some small data sets by hand. It clarifies the process very quickly. It is common for stat programs to offer to analyze groups with unequal numbers. But what do you do when one column has 12 numbers in it and the other one has 10?
Practice Problems
Simulations and opportunities to practice items so you can get familiar with doing calculations, and be able to check your work.
Computers, Calculator & Women
In the future, we should discuss how all calculating was done by people, mostly women. Before there were machines, computer was a job title.
Start At Square One
A video series about all the steps before calculating. All are on YouTube but linked here so you don’t have to hint for them.
if you know nothing about statistics, this is a great place to start. No calculating, no formulas, just thinking. There is a lot to do before picking up a calculator or booting up a computer. Square One starts at the very beginning.
Here’s what is in each square:
- Square 1: Think up a theory
- Square 2: Do a literature review
- Square 3: Select variables
- Square 4: Operationally define your variables
- Square 5: Pick a design
- Square 6: Decide who to study
- Square 7: Randomly select your subjects
- Square 8: Prepare your materials
- Square 9: Write a proposal
- Square 10: Conduct the study. Informed consent.
- Square 11: Make a data table (data matrix)
- Square 12: Decide how you are using numbers (levels of measurement)
- Square 13: Graph it
- Square 14; Find the center of the distribution
- Square 15: Find the edges of the distribution; dispersion. Announced
Examples of Using Statistics
- Netflix uses stats to target you
- What type of error am I making
- Why we can predict stars but Wall Street
- Baseball Stats
- Not your average American city
- Statistics should be fun
Resources
Formulas, sample tables and other thing that might be helpful.
Review
Nothing exciting, just a list of terms you should understand.
Final Exam
Just for fun, there is a test you can take to check your progress. There are multiple choice items, simulations and calculating items. Answers are given. No grades, sorry.
Measurement
Want to jump ahead?
- What is statistics?
- Ten Day Guided Tour
- How To Calculate Statistics
- Start At Square One
- Practice Items
- Resources
- Final Exam
Book
Statictics Safari
Photo by Markus Krisetya on Unsplash
