stats review Flashcards
levels of measurement (in order lowest to highest)
nominal, ordinal, interval ratio
nominal
numbers or letters assigned to the object serve as labels for identification or classification _→ used to categorize data into categories (lowest)(qualitative)
Basic comparisons: identity
Examples: male/female, user/non user, occupations, uniform numbers
Measures of average: mode
ordinal
arranges objects or alternatives according to their magnitude in an ordered relationship. Ordinal only indicates relative size differences between objects. Puts variables into natural order → rating, ranking (qualitative)
Basic comparisons: order
Examples: brand preferences, social class, hardness of minerals, quality of lumber
Measures of average: median, mode
interval
arranges objects according to their magnitudes and also distinguishes in units of equal magnitude (quantitative)
Basic comparisons: order
Examples: temperature, grade point average, brand attitude
Measures of average: mean, median, mode
ratio
has absolute rather than relative quantities, and an absolute zero where there is the absence of an attitude → periods of time, $ spent, # of items purchased (highest) (quantitative)
Basic comparisons: comparison of absolute magnitudes
Examples: sold, # of purchases, age, income
Measures of average: mean, median, mode
central tendency
mean, median, mode, range, standard deviation, variance, z-score
mean
the average. Sum of numbers/amount of numbers
median
the middle score
mode
the most frequent score
range
max score – min score. Distance between the smallest and largest values in the set
standard deviation
the square root of the largest values in the set of the variation
Deviation scores: the differences between each observation value and the mean → Di = Xi - mean
Average deviation: (not super informative)
Mean squared deviation
★sample standard variation
variance
given is squared units → population σ squared, sample s squared
Sample variance
z-score
how much a single score is from the mean (in SD units)
Variability
pearson correlation
is a numeric measure of the strength of the linear association between two continuous variables
- interval level data
-We can also use the pearson r for one dichotomous and one continuous
spearman correlation
-coefficient degree of association between two ordinal variables
-ordinal level data
t-test
IV: Categorical (2 levels/groups) DV: interval or ratio
-interval level data
null hypothesis
no difference between the 2 variables
alternate hypothesis
some difference between the 2 variables
degrees of freedom
type 1 error
-when you falsely reject null hypothesis
-You rejected the null hypothesis.
BUT when other researchers replicated your study, they found no difference between the groups (no significance).
-E.g. False positive covid test result (you don’t actually have covid –
null; but test says you are)
type 2 error
-when you falsely don’t reject the null hypothesis
You did not get stat. significance and therefore don’t reject the null.
Other researchers replicate your study and find that there is
significance.
-typically happens due to small sample/small effect sizes
-Bigger sample = powerful telescope
-E.g. False negative covid test result. (you have covid, but test says you
don’t)
one way ANOVA
-ANOVA stands for Analysis of Variance.
-When you have one categorical IV with 2 or more levels/groups
-When you have interval/ratio DV
-“One-way” means “one independent variable”
-It’s to compare the means for 3 groups or more.
IV: categorical variable (manipulation) (3 levels or more)
DV: either interval or ratio level variable
-need at least interval level data, ratio also works
-reduces the likelihood of type 1 error
chi-squared test
IV: Categorical DV: Categorical
-looking at frequencies
factorial ANOVA
When IV is categorical, you can run several tests:
* IV (2 categories: cat vs dog person) & DV (interval/ratio:
extraversion scores) 🡪 t-test
* IV (3 categories: coffee vs tea vs water) & DV (interval/ratio:
exam score) 🡪 1 way ANOVA
* But what if you have 2 IVs?
* If you want to see whether another variable also affects the DV?
Both IVs: Categorical
DV: Interval or ratio
-need at least interval level data, ratio also works
main effects
-whether each IV induces any differences in DV (on their own)
-If you have 2 IV, you could have 2 Main Effects.
-2 main effect hypotheses.
-Main effect 1: How ad length (IV1) affects ad recall (DV)
-Main effect 2: How medium (IV2) affects ad recall (DV)
interaction effects
-whether both IVs induces any differences in DV (together)
-You will have an interaction effect between IV1 x IV2
-1 Interaction is possible, so 1 interaction hypothesis.
-How does the combined effect of ad length and medium (IV2 *IV2) affect ad recall (DV)
