05 - basic statistics concepts Flashcards
Why we need statistics (2 reasons)
OBJECTIVE way of interpreting a collection of observations
REDUCE data to useful value that represents a trait about the data
Categorical measurements
Qualitative
( “which type” and “which category”)
Continuous measurements
Quantitative
“how much” and “how many”
4 different scales of measurement
Nominal
Ordinal
Interval
Ratio
Which 2 scales are categorical
Nominal
Ordinal
Which 2 scales are continuous
Interval
Ratio
Nominal scale
“Name”
Associated with categorial data
Ordinal scale
“Order”
Associated with categorical data
Any rank ordering
Limitation of ordinal scale
Don’t always know the amount of difference between each piece of data
Interval scale
“equal intervals”
Associated with continuous data
Has all the properties of ordinal data plus equality of units
May contain an arbitrary zeron
Ratio scale
Ratio statements can be made
Associated with continuous data
Has all the properties of interval scale plus an absolute zero
What is an arbitrary zero?
Does not reflect the absence of the trait being measured
What is an absolute zero?
Absence of the trait
Summary - nominal
Values are named
Summary - ordinal
Values are named and ordered
Summary - interval
Values are named and ordered and have equal intervals
Summary - Ratio
Values are named and ordered and have equal intervals and have an absolute zero
Statistical foundations of measurements theory (7)
- Frequency distribution
- Mean
- Variance
- Standard deviation
- Normal curve
- Correlation coefficient
- Standard error of measurements
What is frequency distribution?
Number of times each scores is represented in the data set
What is mean?
Sum of the observation divided by the number of observations
What is variance?
Measure of variability of the data set
What is standard deviation?
Square root of the variance
What is normal curve?
Symmetric frequency distribution
Z-score
What is correlation coefficient?
The degree of linear relationship between two variables
What is standard error of measurements (SEM)?
Relate the given score to the “true” score
Determine the amount of measurements error of a tool on a set of repeated measures
Descriptive statistics
Used to describe the group from which data is collected
No intention to generalize beyond that group or point in time
Inferential statistics
Used when making generalizations or inferences to other groups or variables
Population
All-inclusive group
Sample
Representative subset of the population
Random samples
The sample should be selected randomly so that it represents the larger population
Stratified random sampling
When the population has subgroups and we want to sample proportionately from those subgroups
Convenience sample
Random sampling is not always possible
However, we should still aim for the sample to be representative
Randomization into groups
Within the sample, people should be randomly assigned to groups
