Unit 1 Flashcards
5 Properties of Quantities
- Name
- Procedural statement
- Number
- Units
- Symbol
Nominal-scaled Quantities and Example
Form of categories that can take on one or more category, but have no order. Mathematical operations on values make no sense.
Ex) Giving a number to qualitative measurements.
Blue eyes = 0101
Green eyes = 100
Brown eyes = 001
Ordinal-scaled Quantities and Example
Quantities that take the form of categories that can be ranked. The relative differences matter, but not quantitative differences. Mathematical operations make no sense.
Ex) frequency of bird to window collisions (rarely, frequently, never), and stage of log decomp.
Interval-scaled Quantities and Example
Quantities with values that have an order. Units are equal size, can be negative, and the distance between measurements is classified, ordered and specified. Differences between values matters, but ratios matters, but rations of 2 values have no meaning.
Ex) A unit in Celsius temperature is 1/100 the differences between freezing and boiling, but a change from 1 to 2 degrees does not mean the temperature has doubled.
Ratio-scaled Quantities and Example
Quantities are classified, ordered, and specified between measurements and have a natural zero. They cannot be negative (negative means an absence of quantity). There are equal intervals between points and mathematic operations are possible.
Ex) length, area, population, Kelvin scale in Temperature
Define Units
How quantities are scaled
Define Dimensions and give example
Categories of units that can be scaled with one another using multiplication or division
Ex) Length is a dimension; cm/ft are units
Ex) Mass is a dimension; kg/lbs are units
What is a derived quantity made of?
A combination of dimensions
Dimensional Homogeneity
Physically meaningful equations that describe relationships between quantities that must be dimensionally homogeneous
Dimensional Homogeneity Rules
- Dimension on one side must equal other side
- Multiplying, dividing, and giving quantities a power most be possible in all dimensions
- Adding and subjecting may only be done between quantities of identical dimensions
Normalized Quantities and Examples
Normalizing quantities is the process of dividing some scaled quantity by a standard, total,or reference value of the same frequency. No units because working with same units
Ex) percentage, frequency, concentration, probability, map scales
Median
the numerical value separating the higher half of the data from the lower half of a data sample or population
Mode
the numerical value that is most common in a data sample or population
Population Variance
THe amount by which individuals in a population differ from the population mean.
OR
The average of the squared deviations from the mean
Sample Variance
A statistic used to estimate population variance
Standard Deviation
square root of variance as population standard deviation or sample standard deviation
What two parameters define the shape of normal distribution?
mean and variance
Z Score and Example
The number of standard deviations the value is away from the mean.
Ex) When the mean of tree height is 90 m, a tree that is 70 m tall would have a Z score of -2.
Regression
A statistical process for estimating the relationships among variables
Linear Regression and Formula
Assumes that there is a linear relationship between a dependant variable and an independent variable.
yi = b0 + b1xi
y = output
x = input
b0 = y intercept
b1 = slope
Correlation coefficient (r)
Measures the strength and the direction of a linear relationship between two variables
Coefficient of Determination (r^2)
Gives the proportion of the variance of one variable that is predictable from the other variable.
Coefficient of Determination (r^2)
Gives the proportion of the variance of one variable that is predictable from the other variable.
Pearson’s R
Correlation coefficient that is a number that indicates two variables are linearly related.
Measures both strength (value) and direction (+/-)
