Ordinal Data:

Need help with ordinal data??

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• Ordinal data
• classified into categories within a variable that has a natural rank order.
• However, the distances between the categories are uneven or unknown.
• For example, the variable frequency of physical exercise can be categorized into the following:
• 
  
  
  
  

There is a clear order to these categories, but we cannot say that the difference between never and rarely is exactly the same as that between sometimes and often - therefore the scale is ordinal.

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• Ordinal is the second of four hierarchical levels of measurement
• nominal, ordinal, interval, and ratio
• Nominal data differs from ordinal data because it cannot be ranked in an order. 
• Interval data differs from ordinal data because the differences between adjacent scores are equal.

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Examples of Ordinal Scales:

• In social scientific research, ordinal variables often include ratings about opinions or perceptions, or demographic factors that are categorized into levels or brackets such as social status or income.
• Language ability
• beginner
• intermediate
• fluent
• level of agreement
• strongly disagree
• disagree
• neither agree nor disagree
• agree strongly agree
• Income level
• lower level income
• middle-level income

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How to Collect Ordinal Data 

• ordinal variables are usually assessed using closed-ended survey questions that give participants several possible answers to choose from. These are user-friendly and let you easily compare data between participants.

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Examples of Ordinal scale survey questions

• what is your age
• 0 to 18
• 19 to 34
• 35 to 49 
• 50 plus
• what is your education level
• primary school
• high school
• bachelors degree
• master's  degree
• PhD
• In the past three months, how many times did you buy groceries online
• none
• 1 to 4 times
• 5 to 9 times
• 10-14 times
• 15 or more times

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Likert Scale Data

Ordinal data is often collected using Likert scales. Likert scales are made up of 4 or more Likert type questions with continuum of response items for participants to choose from

Example of Likert-type questions 

• How frequently do you buy energy-efficient products?
• never
• rarely
• sometimes
• often
• always
• How important do you think it is to reduce your carbon footprint?
• not important
• slightly important
• important
• moderately important
• very important
• But it's important to note that not all mathematical operations can be performed on these numbers
• Although you can say that two values in your data set are equal or unequal
• you can say that one value is greater or less than another.
• You cannot meaningfully add or subtract the values from each other.
• This becomes relevant when gathering descriptive statistics about your data.

How to Analyze Ordinal Data⏹️⏹️⏹️⏹️⏹️⏹️

• Ordinal data can be analyzed with both descriptive and inferential statistics.

Descriptive Statistics⏹️⏹️⏹️⏹️⏹️

• With Ordinal Data
• the frequency distribution in numbers or percentages. 
• the mode or the median to find the central tendency
• the range to indicate the variability
• Example 
• You ask 30 survey participants to indicate their level of agreement with the statement below
• Regular physical exercise is important for my mental health.
• strongly disagree
• disagree
• neither disagree nor agree
• agree
• strongly agree

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To get an overview of your data, you an create a frequency distribution table that tells you how many times each response was selected

To visualize your data, you can use a bar graph

• Plot your categories on the x-axis and the frequencies on the y-axis
• Unlike nominal data,
  
  
  the order of categories matters when displaying ordinal data.

Central Tendency⏹️⏹️⏹️⏹️⏹️⏹️⏹️⏹️

The central tendency of your data is where most of your values lie

• The mode, mean, and median are the three most commonly used measures of central tendency.
• the mode can almost always be found for ordinal data
• the median can only be found in some cases.
• The mean can not be computed with ordinal data
• finding the mean requires you to perform arithmetic operations like addition and division on the values in the data set
• the differences between adjacent scores are unknown with ordinal data, these operations can not be performed for meaningful results.
• the mode of your data is the most frequently appearing value.
• the mode of the data set is agree

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Medians

• for odd and even numbered data sets are found in different ways
• in an odd numbered data set the median is the value at the middle of your data set when it is ranked.
• In an even-numbered data set, the median is the mean of the two values in the middle of your data set.

• Order all data values and locate the middle of your data set to find the median
• Since there are 30 values, there are 2 values in the middle at the 15th and 16th positions since both values are the same the median is Agree
• If the two values in the middle were Agree and Strongly agree instead, then you could not find the mean since the mean of the two values can't be found even if you coded them numerically - so in this case there is no median.

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Variability

• Find the minimum, maximum, and range of your data set
• code your data by assigning a number to each of the responses in order from lowest to highest.
• 1 strongly disagree
• 2 disagree
• 3 neither disagree nor agree
• 4 agree
• 5 strongly agree

The minimum is 1 and the maximum is 5

1. The range gives you an idea of how widely your scores differ from each other.
2. From this information, you can conclude there was at least one answer on either end of the scale.

From this information, you can conclude there was at least one answer on either end of the scale.

Statistical Tests

1. Inferential statistics will help you test scientific hypotheses about your data
2. The most appropriate statistical tests for ordinal data focus on the rankings of your measurements and these just happen to be non-parametric tests
3. Parametric tests are used when your data fulfills certain criteria like a normal distribution
4. Parametric tests assess means
5. non-parametric tests often assess medians or ranks.
6. There are many possible statistical tests that you can use for ordinal data.
7. The one you choose depends on your aims and the number and type of samples

• 
  

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References

 Bhandari, Pritha. “Ordinal Data: What Is It and What Can You Do with It?” Scribbr, 12 Aug. 2020, www.scribbr.com/statistics/ordinal-data/.

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Requiem for a Teaspoon: A Caffeinated Elegy

The Caffeinator: Dawn of Toxicity

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Pure and highly concentrated caffeine products pose a significant public health risk due to their potency and potential for overdose. These products, often sold in bulk and packaged without precise measuring tools, contain dangerously high levels of caffeine - a single teaspoon of powder can be equivalent to 28 cups of coffee.  (Nutrition, 2023)

According to the FDA's 2023 article  (Nutrition, 2023), common side effects like nervousness are magnified, and potentially fatal consequences like seizures and rapid heartbeat can occur. Consumers unaware of this potency compared to regular coffee are particularly at risk. The FDA actively monitors and takes action against these products, including seizure and injunctions according to their recently published article (Nutrition, 2023). 

According to Nutrition (2023), the following is a timeline on the FDA's action on pure and highly concentrated caffeine:

1. On September 1, 2015 - the FDA issued warning letters to five distributors of pure powdered caffeine products.
2. March 2016 - The FDA issued two additional warning letters
3. On April 13, 2018, the FDA released guidance for the industry on highly concentrated caffeine in dietary supplements
1. This document provides guidance for companies who manufacture, market, or distribute dietary supplements containing pure or highly concentrated caffeine or are considering doing so, to help them determine when a product is considered adulterated and illegal by the FDA

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 References

1. Nutrition, C. for F. S. and A. (2023). Pure and Highly Concentrated Caffeine. FDA. https://www.fda.gov/food/dietary-supplement-ingredient-directory/pure-and-highly-concentrated-caffeine

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Decoding the Data Whisperer:

 A Beginner's Guide to Z-Scores

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Imagine you're in a classroom full of students who all took the same exam. You scored 75, but how does that compare to everyone else? Did you ace it or just barely scrape by? Enter the z-score, a powerful tool that helps you understand your position within a dataset.

Think of z-scores as a translator. It takes your raw score and converts it into a universal language, telling you how many standard deviations away you are from the mean or average of the group. S standard deviation is basically a measure of how spread out the data is.

The lowdown on z-scores:

The Formula:

Interpretation:

Positive z-score means you scored above the mean, The higher the z-score, the further above the mean you are. For example, a z score of 2 means that you are 2 standard deviations above the average.

A negative z score means that you scored below the mean. The more negative the z-score, the further below the mean you are. 

A z-score of 0 then you are right on the mean.

Benefits of Z-Scores:

1. you can compare apples to oranges. You can compare data from different sets with different units. Imagine comparing your exam score to your friend's height. Z-scores make it possible by putting both scores on the same scale.
2. Spot outliers: Extreme values that deviate significantly from the rest of the data can be easily identified with z-scores. A z-score far above or below the others might indicate an error or a unique case that deserves further investigation.
3. Predict probabilities: Knowing the z-score and the properties of the normal distribution-  the bell curve-, you can estimate the percentage of the population that scored lower or higher than you.

For Whom the Bell Curves

From Gambling Odds to Universal Truth

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Have you ever wondered why test scores, heights, and even plant sizes seem

to follow a predictable pattern? The answer lies in a mysterious bell-shaped curve known as the normal distribution. But this ubiquitous curve was not just handed down on a silver platter - it emerged from the mind of a brilliant mathematician named Abraham De Moivre in the 18th century (Nesselroade & Grimm, 2020).

• De Moivre, a friend of legends like Halley and Newton, was not interested in boring old graphs. He was fascinated by the odds of chance, specifically the probability of flipping a coin a thousand times and getting between 500 and 600 heads. As he crunched the numbers, something magical happened, the results began to form a bell-shaped curve.
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• But how did he get that iconic formula with its mysterious constants like pi and e? Well, that's a secret lost to the writing style of the time, where results were proudly displayed but methods remained tightly under wraps (Nesselroade & Grimm, 2020). It's a tantalizing glimpse into De Moivre's mind, bending seemingly unrelated fields like gambling and geometry to birth a universal truth. 

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While De Moivre laid the groundwork, others helped the bell curve ring far and wide. Thomas Simpson extended it to continuous measurements like star positions, proving that averaging multiple observations in the sky is the key to minimizing error. Then came Pierre Leplace with his Central Limit Theorem, the grandaddy of statistics, showing that the average of many samples from a population tends to follow a normal distribution  (Nesselroade & Grimm, 2020).

  This opened the door to using the curve for all sorts of hypothesis testing and probability calculations

And who can forget Carl Gauss, the mathematical prodigy who discovered an error in his father's payroll at the age of 3 (Nesselroade & Grimm, 2020)? He not only popularized the normal distribution but also used to predict the reappearance of a lost asteroid with just a handful of observations. Talk about putting your theories to the test!!

Today, the normal curve is the bedrock of statistics, guiding everything from test score analysis to market research. It is a testament to the power of human curiosity and the unexpected connections that can lead to groundbreaking discoveries. So, the next time you see a bell curve, remember De Moivre, Simpson, Laplace, and Gauss - the pioneers who unlocked the secrets hidden within the randomness of numbers.

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 References

 Nesselroade, P. K. & Grimm, L. G. (2020). Statistical applications for the behavioral and social sciences (2nd ed.). Soomo Learning. https://www.webtexts.com