Introducing Statistics: Random and Non-Random Patterns? Chapter Notes | AP Statistics - Grade 9 PDF Download

Again and again, data proves that probability and statistics are powerful tools that allow us to quantify and analyze the likelihood of events occurring in real-life situations. By using statistical analysis, we can make predictions and draw conclusions about the likelihood of certain events happening based on data and probability theory.
For example, if we want to know the likelihood of flipping a coin and getting heads 10 times in a row, we can use probability and statistical analysis to calculate the probability of this event occurring. We can also use statistical analysis to make predictions about the likelihood of other events occurring, such as the probability of a particular stock increasing in value over a certain period of time or the probability of a particular medical treatment being effective for a certain condition.
Probability and statistics allow us to quantify and analyze the likelihood of events occurring in real-life situations, which can help us to make informed decisions and better understand the world around us.

Daily Experiences

Every day, we see things that happen simultaneously to the point we question the possibility of that event happening again. We simulate that event over and over in our heads, looking at all the possible outcomes. We conclude sometimes that some things happen at random as the overall probability of that event is extremely low.
We can turn to statistics and quantify the actuality of some real-life experiences that we unconsciously or consciously question.

Statistical Significance

Learning how to differentiate between random and non-random patterns when analyzing data is important, as this can help you to draw more accurate conclusions about the data and the underlying phenomena being studied. Even if there is a pattern, that doesn’t always make the data unbiased or reliable enough to build a conclusion. Patterns don’t always mean that the data variation isn’t random. That doesn't exclude error at all.
Random patterns occur when the data variations are not systematic and cannot be predicted with any degree of certainty. Random patterns are often associated with random error, which is error that is introduced into the data due to random, unpredictable factors.
On the other hand, non-random patterns occur when the data variations are systematic and can be predicted with some degree of certainty. Non-random patterns are often associated with bias, which is a systematic error that is introduced into the data due to a particular factor or set of factors as you might recall in Unit 3.
It's important to be aware of the potential for both random and non-random patterns in data, as this can help you to identify and control for any sources of error or bias that may be present. This can help you to draw more reliable conclusions about the data and the underlying phenomena being studied!

Examples, Examples, Examples: Random vs. Non-Random Patterns

Here are some examples of random patterns in statistics:

• The results of flipping a coin: When flipping a coin, the outcome (heads or tails) is determined by random factors such as the force applied to the coin and the surface it lands on. The probability of getting heads or tails is the same on each flip, and it is not possible to predict with any degree of certainty which outcome will occur. This is an example of a random pattern.
• The heights of students in a classroom: The heights of students in a classroom are likely to vary randomly, with some students being taller or shorter than others due to a variety of factors such as genetics, nutrition, and environmental factors. The distribution of heights in a classroom is likely to be random, with no systematic pattern or bias present.
• The results of a randomized controlled trial: In a randomized controlled trial, participants are randomly assigned to either a treatment group or a control group, and the results of the trial are analyzed to determine the effectiveness of the treatment. The randomization process ensures that any differences between the treatment group and the control group are due to the treatment being tested, rather than any other factors.

Here are some examples of non-random patterns in statistics:

• The relationship between education level and income: There is often a strong, non-random relationship between education level and income, with individuals who have higher levels of education generally earning more than those who have lower levels of education. This relationship is systematic and can be predicted with some degree of certainty, making it a non-random pattern.
• The relationship between age and heart disease risk: There is a well-established, non-random relationship between age and the risk of developing heart disease, with the risk increasing as a person gets older. This relationship is systematic and can be predicted with some degree of certainty, making it a non-random pattern.
• The relationship between pollution levels and respiratory illness rates: There is often a non-random relationship between pollution levels and the incidence of respiratory illnesses, with higher pollution levels being associated with higher rates of respiratory illness. This relationship is systematic and can be predicted with some degree of certainty, making it a non-random pattern.

See if you can tie in learnings from Unit 3 with this unit moving forward! One of the most effective ways to learn is to make connections between two seemingly unrelated things.

Key Terms to Review 

• Bias: Bias refers to a systematic error that leads to an incorrect or misleading representation of a population or phenomenon.
• Probability Theory: Probability Theory is a branch of mathematics that deals with the likelihood of different outcomes in uncertain situations.
• Random Error: Random error refers to the unpredictable variations that can occur in measurements or observations.
• Randomized Controlled Trial: A Randomized Controlled Trial (RCT) is a scientific experiment that aims to reduce bias when testing the effectiveness of new treatments.
• Statistical Analysis: Statistical analysis is the process of collecting, examining, and interpreting data to uncover patterns, trends, and relationships.
• Systematic Error: Systematic error refers to consistent, repeatable inaccuracies in measurements or data collection methods.