Variables
Variable is a trait or characteristic that takes on different values or levels
Constant does not vary
- Researchers distinguish between variables.
- Independent (IV) v. Dependent (DV) Variables
- think in terms of Cause (IV) and Effect (DV)
Term IV has assumed different meanings in various areas of behavioral sciences.
- Some investigators restrict the definition to a variable that is experimentally manipulated in the context of an experiment.
- We adopt a more general definition of independent variable as any variable that is presumed to influence a second variable.
Measurement
Involves translating empirical relationships between objects into numerical relationships.
Measurement Hierarchy (see handout)
Quantitative and Qualitative Measures
- Qualitative cannot be ordered, only classified according to qualities possess (Nominal)
- Quantitative can be ordered based on values along dimension (Ordinal, Interval, Ratio)
Populations and Samples
- Population aggregate of all cases to which one wishes to generalize
- Sample subset of the population.
- Representative Sample when we select a sample in order to make a statement about a population on a given dimension, we want to ensure we are using a representative sample of the population.
- Random Sample procedure for approximating a representative sample.
- Essential characteristic every member of the population has an equal chance of being selected for the sample
Parameters v. Statistics
- Parameters indexes based on entire population
- Statistics indexes based on data from sample of the population.
Descriptive and Inferential Statistics
- Descriptive Statistics involve the use of numerical indexes to describe either a population or a sample.
- Inferential Statistics involve taking measurements on a sample and then, from the observations, inferring something about the population.
Mathematical Preliminaries: Summation Notation
Suppose we have a measure of the number of days of work each of five individuals missed in the past month, the score on this variable are as follows:
|
X (# days missed) |
Y (money earned each day) |
|
1 |
100 |
|
3 |
200 |
|
5 |
300 |
|
7 |
400 |
|
9 |
500 |
Suppose we want to sum the five scores on variable X to determine total number of months worked by the five individuals.
- In stats, we have a short hand way of writing instructions to sum a set of scores, summation notation.
- In this instance: 
Second expression will encounter: 
A third summation expression is: 
A fourth summation expression is: 
A fifth summation term we will encounter is: 
A sixth summation term we review is: 
Rounding
- The number of decimal places used in reporting a statistic will differ depending on the nature of the variable being reported.
- Most commonly, reported to two decimal places
- Intermediary calculations should be done using at least one decimal place beyond the number of decimal places plan to use in final answer.
- If you are performing computations on a calculator, rounding error can be substantially reduced by keeping all digits shown until you round the final result.
These two rules you should already know:
1. If the remainder to the right of the decimal place you wish to round to is greater than one-half a measurement unit, increase the last digit by one.
2. If the remainder to the right of the decimal place you wish to round to is less than one-half a measurement unit, leave the last digit as it is.
**This is new rule you need to know! (Does not replace other rules only when the last digit is a 5, so you cant just round up or down easily)
3. If the remainder to the right of the decimal place you wish to round to is exactly one-half a measurement unit, leave the last digit kept as it is if it is an even number, but increase it by one if it is an odd number.
- Note that when this rule is used, the last digit of the answer will always be an even number.
- According to this rule, 10.345 is rounded to 10.34 because the 4 in the hundredths place is an even number, and 10.335 is also rounded to 10.34 because the 3 in the hundredths place is an odd number.
- The purpose of the rule is to avoid a bias in rounding up or down across a large set of numbers; with the rule, approximately half the time you will round up and half the time you will round down.
