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Basic Mathematical Concepts
STAT Chapter 2
PSYC 201: Psychological Research I
Math as a Recipe
Necessary for the recipe and for statistics:
The ingredients (variables) The amounts of each (numerical values) The operations (addition, subtraction, multiplication, and division) The order you do things
Check out the Math Review in a Nutshell for a
refresher (it’s on my website)
Here are a few of the refreshers
Order of Operations Do all work inside of parentheses first Perform multiplication and division before performing addition and subtraction Do summation first, then perform addition/subtraction
Rounding Round as usual except when rounding off a number ending in a five (5). If the number is larger than five, round up; if the number is less than five, round down If the number immediately preceding a five is odd, round up. If the number immediately preceding a five is even, round down
and, a few more
Decimals When working on a problem, keep at least 4 decimal places throughout. When you get to the final answer, you should round it to 2 decimal places When multiplying, the answer has the total number of decimal places as the total number in the two multipliers
Fractions and Decimals It is best to convert fractions to their decimal equivalents as soon as permitted under the rules of mathematics. For example, to convert 1/5, divide 1 by 5, which yields
There are several more to do with fractions
Summation Notation
Sigma X = ΣX = Sum of X
ΣX 2 = Square the X values first, then sum
them up
(ΣX)^2 = Sum up the X values first, then square
them
An example
Student X Y
Number of incorrect answers on the Stat exam
Level of math/statistics anxiety
Nominal scales
PROPERTIES: Differences or naming Categorizing events into one of a number of discrete categories
OPERATIONS: Equal / not; member / not a member
EXAMPLES:
Religious preference Eye color Disposed of cigarette appropriately (yes or no) Type of public display of affection (hug, kiss, etc.)
Ordinal scales
PROPERTIES: Differences, plus ordering or ranking the events to be measured
OPERATIONS: Equal or not, and greater than / less than or rank ordering
EXAMPLES:
Top five contestants in a speech contest Rank order your preferences for fast food
Interval scales
PROPERTIES: equal intervals Differences, rank ordering or magnitudes, plus specifying how far apart events are on a given dimension
OPERATIONS: Equal or not, greater than / less than, AND addition, multiplication, subtraction, division
Examples: Temperature (Fahrenheit or Celsius, because no true 0) Calendar time Scores on an achievement test (e.g., SAT)
Ratio scales
PROPERTIES: True zeros Differences, magnitudes, equal intervals, PLUS this scale has an absolute zero point
OPERATIONS: Equal or not, greater than / less than, addition, multiplication, subtraction, division, PLUS formation of ratios of values
Examples: Temperature (Kelvin, because it has absolute zero) Time (e.g., in seconds) Length, age, weight, frequency, etc.
What are some appropriate statistics?
Percent variability; same inferential tests as Interval
Find ratios, fractions
Ratio
Mean; SD; etc. Correlation; ANOVA; t-test
Find distances or intervals between units
Interval
Median; Percentiles
Establish rank order
Ordinal
Number of cases; Mode; Chi Square
Identify and classify
Nominal
