Mutually Exclusive Categories

Hello all, in this post we will address the following question "What do we mean by mutually exclusive categories?"

Events are mutually exclusive if it is impossible for them to happen at the same time. If there are two outcomes that can occur for a given event it can be one or the other, but not both. These outcomes do not and cannot overlap in any way. Another way of thinking about it in terms of logic is if two categories are mutually exclusive they cannot both be true at the same time – they are disjoint.

Examples include the following:

Making at turn while driving. If you reach the end of a block you can go straight, turn right or left. You cannot do a combination of both. Each event will occur and must occur without the other 2 happening.

The colors on a stoplight can only be red, yellow, and green. It can only show one color at a time.

A common example is a coin toss, it can be heads, or it can be tails, but it cannot be both at once.

If today is Saturday, today cannot be Monday. These are mutually exclusive events in that Today is Saturday, but it cannot also be Monday.

Rolling dice, you can roll a 5 or 2 but not both at the same time.

The radio cannot be both on and off at the same time. 

Levels of Measurement, Nominal, Ordinal, Interval and Ratio....Oh my?

Data can be classified according to levels of measurement. The level of measurement determines how data should be summarized and presented. There are four levels of measurement, nominal, ordinal, interval and ratio. 

The nominal level describes a characteristic that has no order and can be classified or counted examples include categories or color. The next level is the ordinal level which can be ranked however you cannot conclude how much better one rank is from another examples include good better best. Moving up the next level is the interval level which includes all characteristics of nominal and ordinal level data but now the intervals and differences between the levels are more meaningful examples include temperature in Fahrenheit. However one notable characteristic of the interval level is the value of 0 does not denote absence of data, rather it is just the point on the scale examples for this are shoe size ring size or dress size where there is no natural zero. With interval level data while the measurements between the intervals remain consistent their ratios are not. The final level is the ratio level, differences and ratios in this level are meaningful. Furthermore the value zero is also meaningful if you have zero of something there is none of it. Examples of ratio data often consist of counts.

Nominal	Ordinal	Interval	Ratio
·       Hair color ·       Sex ·       Religious affiliation ·       Gender ·       Eye color ·       Place of birth ·       Race ·       Department ·       Car Manufacturer ·       Demographic or qualitative data ·       Color ·       Shape	·       Grades/Performance at school, A/B/C/D/F Severity level: low, medium, high Rating systems centered around inferior, poor, good, excellent, superior ·       "Bad", "Okay", "Good", and "Great" ·       Ranks and Ratings	·       Shoe size ·   Fahrenheit and Celsius temperatures ·  Clothing sizes – ie pants size ·  Ring Size ·  Bra Size	·       Number of students in a class ·       Age ·       Disposable income ·       Kelvin temperatures ·       Distance to work ·       Number of patients seen by a doctor ·       Amount of Money

Descriptive vs Inferential Statistics

Welcome, in this post we will explore some of the differences between descriptive and inferential statistics.

Descriptive statistics – can be thought of as stating a fact – it involves organizing, summarizing, and presenting data in a well-laid out and informative way. It uses numbers to describe data.  Examples include bating averages in baseball or height or weight averages in a classroom. There are no extrapolations or assumptions. You’re kind of just dealing with what you already have and know. This includes the past and the present. However it cannot provide information about the future. 

Inferential statistics - takes information about a group (the sample) and applies it to the whole (the population) - allows us to understand or make a prediction about the population through a limited set of data. For example you administer a questionnaire to a group of people and use the results from the sample to make decisions and observations about a population. With inferential statistics you make inferences. This in part is because getting all the data from a population or census may prove impossible, difficult, expensive, time consuming, or destructive. Inferential statistics is fantastic for extrapolating and predicting patterns.

What is statistics?

Welcome! In this post we will touch upon the following question, what is statistics?  

"There are lies, damned lies, and statistics" - Mark Twain.

Per google

sta·tis·tics /stəˈtistiks/  noun: statistics

The practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

synonyms:

data, facts and figures, numbers, information, details; informalstats "recent statistics show an increase in allergic reactions"

Statistics is the science of sorting, analyzing, and evaluating information that we encounter in school, at work, and throughout everyday interactions. It requires using skills and understanding to organize, summarize, and analyze data

Per Miriam Webster

1 :  a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data 

2 :  a collection of quantitative data

Statistics is the science of gathering, organizing, and making sense of data in a meaningful way in order to understand the world around us and make informed decisions based on that data. It may be applied to both business and personal activities.

All in all

Statistics is a mathematical method or science used to organize, evaluate and compile data or facts. More specifically statistics refers to the process of collecting, organizing, presenting, analyzing, and interpreting data to help us in making effective decisions. It can be used in any field of work or study and often we use statistics regardless of if we know it or not. Consider it a method of making potentially complicated and hard to understand data easier to understand. 

Statistics are provided to us in many forms and mediums, for example it can be used  in politics to see which candidate is polling better in a particular state, schools and graduation rates, hospitals and infection rates, businesses and seeing what products are more profitable, social media and trends, and more.

Statistics enables us to get as much out of numerical information as possible.  For example it allows researchers to evaluate conclusions derived from sample data. Statistics aids in the process of the scientific method by collecting data, interpreting and analyzing it. It also allows for measures that assess the reliability of conclusion based on sample data even when faced with issues related to variability and uncertainty.  Note that there are different levels of measurements including nominal-level, ordinal-level, interval-level, and ratio-level (see this previous post for reference).

Statistics and its respective calculations look at the data in a new way and make better use of it so that it can assist us in not only business and work-life, but also in our personal decision-making.  Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to allow effective decisions making in business, economics, and everyday life. 

Side note

Statistics can also refer to numerical information such as percentages, outcomes, and ratios.  

Types of Data Measurement Scales

Welcome! In this post we are going to identify examples of measurement or data for nominal, ordinal, interval ratio levels of data.

      

Nominal measurements organizes data into categories that cannot necessarily be arranged in any particular order.  Data at this level tends to be qualitative. Nominal measurements are considered to be the lowest level of measurement and describe data that has no order. Nominal data can be thought of descriptive categories or qualities that can only be counted or classified.  One thing to note is that categories typically must be mutually exclusive meaning the the description or data can only fall into one category. Examples include biological gender, race, hometown, primary language at home, fabric type,  car brand, college, and color IE car colors.

Ordinal measurements - considered to be the next "level of data" in the hierarchy-  organizes data in some order, this order or ranking tends to be relative and the differences in the data values cannot always be determined, nor is it necessarily worthwhile. When you hear ordinal think order. Data categories or ordinal data have some logical order, where the order is based on perceived importance or meaning. The aforementioned categories are mutually exclusive and exhaustive. Examples include rating something as big, bigger, and biggest or A/B/C/D or F grading scales or cancer stages. This type of measurement is also great for questionnaires that ask questions about habits, ie how likely are you to purchase xx again unlikely,  moderately likely, or highly likely.

Interval measurements are similar to ordinal in that you can ascertain  some sort of order but now the differences between data is meaningful, and can always be determined. Interval level data includes all the characteristics of the ordinal level, and the difference between values is a constant size. One thing to note is that with interval measurements there is also no natural zero point or "true zero" - zero doesn't exist in nature. Examples include ring size, year an event happened, pH level, dress size, temperature and shoe size or number of stars in a yelp review. If you wear size 0 clothing it doesn't mean your naked, or that you don't wear clothes.

Ratio measurements, unlike intervals, have a zero starting point, and  differences are always meaningful. Ratio level data includes all the characteristic of the interval level and there is a meaningful zero point. Differences and ratios comprising of ratio level measurements are meaningful and can be used for analysis. Examples  include height, heart beats per minute, amount of money, volume of fluid, number of miles driven, and years of education.