Different scales of measurement
- Nomial Scale
- different categories or groups, no numerical/quantitative properties
- Ordinal Scale
- rank order, but no sense of distance between intervals
- Interval Scale
- equal space between intervals, but no true 0
- Ratio Scale
- equal space between, intervals, and has a true zero
Describing Results
- 3 basic options
- comparing group percentages (nominal)
- correlating individual scores (range of values)
- comparing group means (distant groups)
Frequency Distributions
- Frequency distribution= the number of individuals who recieve each possible score on a variable
- for ordinal or nomial could display pie chart, or bar graph
- for interval or ratio, could do frequency polygon, or a histogram
Descriptive Statistics
- descriptive statistics enable vs to make a prease, concise= statement about the data
- central tendency (what is the sample like overal)
- mean
- median
- mode
- variable
- standard deviation
- variance
- range
Correlation Coefficients: Strength of Relationship
- correlation coefficient= how strongly variables are related to one another
- pearson product moment- correlation coefficent for linear
- scatterplot
- restriction of range: when there’s not much diversity in your sample on one or both of the variables you’re testing
- Pearson r is designed only to detect linear relationships
Effect Size
- effect size= how strongly two variables are associated
- pearson r is one way to indicate this ranges of 0.00 to 1.00
.10 is small, .50 is medium and 1 is large
- pearson r is one way to indicate this ranges of 0.00 to 1.00
REgression Equations
- regression equations used to predict the value of one variable (criterion variable) by using the value of the other variable (predictior)
- multiple correlation/regression) combines several predictor variables to more accurately predict an outcome variable
The Third Variable Prob
Partial correlation is a way to statically control for thrid variables”
restriction of range
when there’s not much diversity in your sample on one or both of the variables you’re testing
Provide and example of nomial, ordinal, interval, and ratio data. Given an example of a variable, be able to identify which type it is
Nominal: Just names or labels, no order.
Ordinal: Ordered categories, but not necessarily equal intervals.
Interval: Equal intervals, but no true zero.
Ratio: Equal intervals and a true zero, allowing for ratio calculations.
What type of data best be summarized by comparing group percentages
nominal data (ie a person’s favorite ice cream flavor)
What type of data would best be summarized by comparing correlating individual scores?
When there are variables that have a range of numerical values (ie the analysis of data on the relationship between location in a classroom and grades in the class)
What type of data would best be summarized by comparing comparing group means?
- use if participants are in two or more groups. Ie, in an expierments designed to study effect of exposure to an aggressive adult, one group might be children who observe n adult “model” behaving aggressively and the control group might be children who do not. Each child then pplays alone for 10 minutes in a room containing a number of toys, while observers record the number of times the child behaves aggressively during play. Aggressin is a ratio scale variable.
What is the purpose of a frequency polygon
Frequency polygons represent the distribution of frequency scores and is most useful when the data represents interval or ratio scales
What is the purpose of a histogram
- displays frequency distribution for quantitative variables
Mean (what is it and when is it an appropriate indicator of central tendency)
x̄
- add all scores and divide by number of scores
- appropriate indicator of central tendency when scores are on interval or ratio scale because actual values of the numbers are used in calculating the statistic
Median (what is and and when is it an appropriate indicator of central tendency)
- score that divides group in half, with 50% scoring above and 50% scoring below
- Used when scores are ordinal
Mode
Most frequent score
- best for nominal data
Standard deviation
, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
- Not used for qualitative data
What info is conveyed in a Pearson product-moment correlation coefficiant (by the number? by the sign?)? What kinds of data is this test appropriate for?
- tells us strength and direction of relationship
- The Pearson r correlation coefficient is used for quantitative data that is measured on an interval or ratio scale
How is correlation coefficient abbreviated?
r
Why is effect size? How is it expressed? What are the advantages of this calculation, compared to similar options?
- refers to the strength of association between variables. Measures the meaningfulness of a relationship or difference between groups. A large effect size means the research finding has practical significance, in other words that an intervention was succesful
- it is expressed by using r^2
- is also sometimes referred to as the percent of shared variance between two variables
- advantage to using it is that it provides a scale of values that is consistent across all types of studies
Multiple Correlation/regression
- combinds a number of predictor avariables to increase the accuracy of prediction of a given criterion or outcome variable
- is a correlation between a combined set of predictor variables and a single criterion variable
- In multiple regression, the correlation coefficient between the predicted and observed values is called the multiple R. The multiple R ranges from 0 to 1, with a small value indicating a weak or non-existent linear relationship between the independent and dependent variables.
- Variable R
What does it mean to ‘partial out’ a third variable? What can doing so tell us about the relationship between our variables of interest?
Partially out a third variable means to isolate the effects of a third variable on two other variables in order to determine if there is a relationship between the two other variables. This is done using a statistical technique called partial correlation:
