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Purpose

Example of when it would be used

provides information about significance of differences between groups

provides information about significance of relationships between variables

provides information about a single sample vs. two or more samples

is parametric or nonparametric

Descriptive Statistics: Mean

The average

Average grades in the class

Mean is different from the median because it is the sum of the data set then divided by the total of the number of the data set. So, the average.

Mean and median are both a type of average

A single sample is getting average of the data set

Two or more samples you are getting mean of all means or the average of all the samples

Parametric

Descriptive Statistics: Median

Midpoint in a data set

Median salary; Middle of a groups salary which different from the mean because low and high salaries could way the average.

The median is different from the mean because it is the midpoint of the data set or sample being used. The mean and median can be the same but rarely

Median and mean are both a type of average

With one set or sample it is simply the midpoint such as 3, 5, 12; 5 is your midpoint.

If there is two sets or samples put all the numbers together and then find the midpoint.

Parametric

Descriptive Statistics: Mode

Value that appears most often

Looking at bar chart of incomes that is mostly around minimum wage then you have a couple that make a million dollars.

Mode shows the top number or numbers that are most used but it can affect both the mean and median.

Mode can affect both the median and the mean

There can be no mode

One mode or numbers: unimodal

Two modes or numbers: bimodal

Three modes or numbers: trim (Smith, 2018)odal

Parametric

Descriptive Statistics: Ratio Variables

Ratio variables are used to show comparisons between two or more samples. They are characterized by having answers that are numbers on a scale; the difference between two samples is expressed as having a numeric value which is significant and where a zero response indicates that there is none of that variable, also known as having a true zero.

 Used for measurements such as height, weight and BP.

 The significance of differences between groups is expressed as a ratio of two measurements that are being compared. For example, a weight of 4 grams is twice the weight of 2 grams, or a 2 to 1 ratio.

 Used to show comparison between two or more variables. Can be used to compute the following: how frequent one variable occurs (counts) compared to another, mean, median, mode, percentiles of variables, add or subtract, standard deviation, and ratio. The difference between variables can be quantified. There is an order to the values on the scale.

One sample demonstrates what value is present. Two or more samples demonstrate comparison.

 Parametric

Descriptive Statistics:

Interval variables

Used for showing comparisons between samples. Characterized by having answers that are numbers on a scale where the difference between two values is significant but where zero does not stand for having no values or data for that category of data.

Temperature measurements in Celsius or Fahrenheit. Zero temperature does not indicate absence of heat. 

  The significance of differences between groups is expressed by comparing the frequency a value occurs in one group compared to the frequency that same value occurs in another group, or the mean median or mode for each group can be compared.

 Can be used to compute the following: how frequent one value occurs (counts) compared to another, mean, median, mode, percentiles, add or subtract, standard deviation. The difference between variables can be quantified. There is an order to the values on the scale. The difference between two or more variables can be computed, such as 40 degrees Fahrenheit is 30 degrees higher than 10 degrees Fahrenheit; but 40 degrees Fahrenheit is not twice as hot as 20 degrees Fahrenheit.

 One sample demonstrates the value that is present. Two or more samples demonstrate comparison.

 Parametric

Descriptive Statistics:

Ordinal variables

Also called ranked variables, is an ordered series of responses where the order matters but not the difference between the values; such as from smallest to largest, best to worst, or 1 to 10 scale.

 Used for assessing patient’s pain level using a scale from 1 to 10, where 1 is associated with no pain and 10 is the worst pain the patient has ever experienced. Pain level of 7 is more painful than a pain level of 4.

Severity of illness is another example.

 Can be used to compare responses between groups through comparing the frequency a value occurs in one group versus another or by computing the median or mode of one group and comparing to another group.

 Can be used to show comparison between variables to compute how frequent a value occurs, median, mode and percentiles. There is an order to the values on the scale.

 A single sample would demonstrate which value on the scale is present. Two or more samples demonstrate comparison.

 Non-parametric

Descriptive Statistics:

Nominal variables

   Represent groups with no obvious rank or order. Often used to label variables that do not have quantitative value. Also can be considered a label.

  Give a value to a description in a survey, such as; what is your hair color

1-Brown

2-black

3-blonde

4-red

So that it is easier to analyze the data.

 Nominal variables are different because it is used as a label not necessarily the actual response or data itself.

 Nominal is a type of variable that can be used with a quantitative data set, similar to interval, ordinal and continuous variables

 This couldn’t be a single sample, it would need to be two or more, as it is for groups with no rank or order

 Parametric

Descriptive Statistics:

Binomial variables

A sub category of categorical variables, when only two choices are possible, either yes or no.

   A coin toss, with only two possible outcomes heads or tails. The statistic would show, the number of times the coin was tossed, and the number of times it lands on heads, and the number of times it lands on tails.

 Binomial is different because there are only two possible options, not infinite such as with continuous

 Binominal is similar because it is used to help take qualitative data and apply it to quantitative capable analysis. Making it similar to the other variables.

 This could be either single or two or more because it represents variables that only have two possible outcomes, so if the outcome is the same every time it could be a single sample.

 Parametric

Descriptive Statistics:

Continuous variables

Any value within a range or numbers, meaning the value is not rounded to the nearest value, it can be fraction or long decimal.

  Recording a person’s weight, it could be 180.00 or it could be 180.0010

Another example is age, the number could be 33years or it could be 33 years 20 days and 3 hours

 Continuous is different because there are never ending possibilities for its value, unlike the other variables that have a defined exact value.

 Continuous is similar because it is a variable used in quantitative data analysis like the other variables.

 This could be a single sample, or two or more because it represents a value with never ending value possibilities, but it could be one value or a group of values.

 Nonparametric

Descriptive Statistics:

Discrete variables

Henry

Inferential statistics: t-tests

Henry

Inferential statistics: ANOVA

 Henry

Inferential statistics: regression analyses

 Carrington

Inferential statistics: various correlational analyses

 Carrington

Inferential statistics: chi-square

 Carrington