The Measurement Flashcards
Descriptive Statistics is what?
Concerned with the presentation, organization, and summarization of sample data
Inferential Statistics is what?
Allows us to generalize or make inferences from our sample of data to a larger group of subjects (population)
What is the population?
The largest collection of persons for which we have an interest at a particular time
What are inferential statistics used to analyze?
Used to make an educated guess about the population parameter
What are descriptive statistics used to calculate what?
Mean from the sample data
What is the Statistic Number?
The number we get from the people (study) we have that we use to estimate the parameter we will have
What is the variable?
What is being observed or measured
What is the constant?
A measurement that stays the same from observation to observation
What are the two categories under Quantitative?
Continuous or Discrete
What are the types of variables under continuous?
Interval and Ratio
What are the types of variables under discrete?
Ratio
What is an interval variable?
Equal distance; arbitrary zero (neg value has meaning)
What is a continuous ratio variable?
Equal distance; meaningful zero (neg value has NO meaning)
What is discrete ratio variable?
Equal distance; variable only exists in whole numbers, meaningful zero
Discrete Variable
Categorical Variable; variable that can have one one of a limited set of values or only whole numbers
What is a Nominal Scale
Categorical; no implied order among the categories
What does dichotomous mean?
2 categories
Can a nominal scale have more than 2 categories?
Yes
What is an Ordinal Scale?
Consist of ordered categories, where the differences between categories cannot be considered equal
What is a Continuous Variable?
Numeric variable; that may take an infinite number of values within a given range
Does a continuous variable posses gaps/interruptions like a discrete variable?
No, continuous variables do NOT need to be whole numbers
What is an Interval Scale?
Continuous; equal distance between values, but the zero point is arbitrary
What is an example of the interval scale?
Temperature, size 0 degrees does not mean nothing
What is a Ratio Scale?
Continuous; has equal intervals between values and a meaningful zero point, which represents absence of the characteristic being measured
What variable can fit as a ratio scale?
Discrete variable when the variable exists ONLY in whole numbers
What does NOIR mean?
Nominal: named categories
Ordinal: same as nominal + ordered categories
Interval: same as ordinal + equal intervals
Ratio: same as interval + meaningful zero
What is the independent variable?
The intervention, or what is being manipulated
What is the dependent variable?
The outcome of interest that should change in response to some intervention
Ex. New medication that treats pain and one of the suspected side effects is nausea, if the patient rates nausea on a scale from 1-10 what is the level of measurement?
Ordinal, there is an order
What is the Central Tendency?
A single value that is considered ‘typical’ of the set of data as a whole
What are the 3 most commonly used measures?
Arithmetic Mean IR
Median OIR
Mode NOIR
What is the mode?
Value that occurs most frequently, can be used with all types of data
What is the only measure of central tendency that can be used with nominal data?
Mode, measure there can be no mode or more than 1 mode
What is the median?
The middle, (n+1)/2 when ordered by smallest to largest
In ordinal data or finite set the interval/ratio data is what?
Median
What are the properties of Median?
Uniqueness: there is only one for a data set
Simplicity: easy to calculate
Not as drastically affected by extreme values
What is Arithmetic Mean?
Interval and Ratio Data
Add all the values and divide by the total number of values
What is the terminology for Arithmetic Mean?
μ = population mean
Σ = sum
Xi = individual observations
N = population size
X̄ = sample mean
n = sample size
What are the properties of the mean?
Uniqueness: only one for a given data set
Simplicity: easily understood and easy to compute
Every value in a set of data enters into computation, it is affected by each value
What is the range?
Difference between the highest and lowest values
Is range a good or poor measurement of dispersion?
Usefulness is limited since it only takes two values into account = POOR measure
What is the Interquartile Range IQR?
Reflects the variability of the middle 50% of the observations
What is the formula for IQR?
Qu - Ql or Q3-Q1
What is Qu or Q3?
Median of upper half
What is Ql or Q1?
Median of lower half
Is IQR a good or poor measurement of dispersion?
Less affected by a few extreme scores = MORE USEFUL measure
What is the Variance?
Measures the dispersion relative to the scatter of the values about their mean
How does dispersion affect Variance?
Values that lie close to their mean = decreased dispersion
If you have 2 dispersions with the same mean number the distribution of the dispersion determines the variance
What is the formula for Variance?
Sample Variance = (1 point in the set - sample mean) ^2
Take all those points and divide by the total number of points in the set n (sample size)
What is Standard Deviation?
The square root of the variance
Simply square root the variance to find SD
What is the difference between Sample SD and Population SD?
The denominator, the “n” vs “N”
Use ‘n’ sample size for Sample SD or use ‘N’ population size for Population SD
What is the measure of central tendency for Nominal Data?
Mode
What is the measure of dispersion for Nominal Data?
Index of Dispersion
0 = when all ratings fall into 1 category
1 - when all ratings are equally divided among categories
What the measure of central tendency for Ordinal Data?
Mode or Median
What is the measure of dispersion for Ordinal Data?
Range or IQR
What is the measure of central tendency for Interval Data?
Mean, Median, or Mode
What is the measure of dispersion for Interval Data?
Range, IQR, or SD
What is the measure of central tendency for Ratio Data?
Mean, Median, or Mode
What is the measure of dispersion for Ratio Data?
Range, IQR, or SD
What is Negative Skewness?
The long ‘tail’ is pointing towards the negative numbers
What is Positive Skewness?
The long ‘tail’ is pointing towards the positive numbers
How is M/M/M ranked in negatively skewed data?
Mode > Median > Mean
How is M/M/M ranked in positively skewed data?
Mean > Median > Mode
