Chapter 13 - Statistics Flashcards
According to lecture, what are the two different branches of statistics?
- descriptive- describes baseline data (the data with which we begin our research)
- inferential- useful for determining relationships among variables and especially when conducting hypothesis tests
What are three most commonly used measures of central tendency?
Mode, median, and mean
What is the formula to calculate median?
(N+1)/2
What is the formula for mean?
x̄=∑X/N (mean equals sum of raw scores divided by total number of cases)
What are the three major measures of dispersion?
Range, average deviation, and standard deviation
What is the formula for standard deviation?
σ=sqrt (∑x^2/N)-x̄^2 (standard deviation equals the sum of the squared deviations from the mean obtained by taking each score and subtraction from the score and squaring each result and summing them, divided by the total number of cases)
What is the normal distribution?
Bell-shaped curve that describes a variety of phenomena
What does a z score measure?
the deviation from the mean relative to the standard deviation
What is the formula for expected frequencies?
((row total)(column total))/total N
What is the formula for degrees of freedom?
(Rows - 1)(Columns - 1)
What are parametric statistics?
it assumes some interval level of measurement and a normal population
What are nonparametric statistics?
Distribution-free statistics in which few assumptions are made regarding the normality of the population
What is the null hypothesis?
H0: states that there is no difference between the groups being compared
What is a t test used to compare?
the sample means of two groups
What is an ANOVA used to compare and what test does it use?
the means of three of more groups; F test
What are the required assumptions for ANOVA?
interval data, random sampling, sample drawn from a normal distribution
What is the Pearson’s r?
shows the relationship between two or more interval-level variables
To employ Pearson’s r, what three assumptions must be met with respect to the data?
- they must be of interval level measurement
- if the joint distribution were to be plotted, the relationship would be linear or resemble a straight line (other statistical measures must be used if relationship is nonlinear)
- the deviations of points from this line must be relatively uniform or demonstrate equal variance
As mentioned in lecture, what are the most common measures of dispersion?
- range
- Interquartile range (middle 50% of a set of scores)
- variation ratio (used with nomial level variables)
- variance (the sum of squared deviations from the mean divided by n-1)
- standard deviation (sqrt of the variance)
According to lecture, what score can we calculate from standard deviation and what properties does this score have?
z score;
it’s symmetrical, unimodal, bell-shaped, and is a theoretical distribution
According to lecture, what is the field of statistics based on?
the field of probability
What is the bounding rule of probability?
the value of any probability must be between 0 and 1
According to lecture, what is the Central Limit Theorem?
it notes the link between samples and populations is the sampling distribution (meaning we don’t have to worry about the shape of the distribution)
According to lecture, what 5 steps that make up hypothesis testing allow us to detect statistically significant differences?
- Specifying assumptions (Stating null and alternative or research hypothesis)
- determining the appropriate statistical test to use (t-test, ANOVA, F stat, r, R, etc.)
- specifying the alpha value, critical value of the statistics, and the critical or rejection region
- calculating the statistic
- making a decision about the null hypothesis and interpreting it
What does the regression equation do?
enables the prediction of one variable on the basis of the value of others
What is Spearman’s rho (rs) and what assumptions does it require?
A measure of relationship for ordinal level data; requires assumptions regarding linearity and random sampling from the population
What does PRE in PRE measure stand for?
proportional reduction in error
What is Gamma?
a measure of relationship for ordinal data that requires the same assumptions as Spearman’s rho (linearity, random samples, and ordinal data)
What is partial correlation?
it looks at the relationship between two variables while controlling for others
What is multiple correlation and what is its symbol?
Involves predicting the dependent variable on the basis of multiple predictors; symbol = R
What is the general formula for multiple regression and what do the symbols mean?
Y’ = a +b1X1 +b2X2+ … +bkXk +e
Y’ - estimated value of Y
a - Y intercept
b - partial slope coefficient
e - residual error term
According to the table given in lecture, what does R stand for?
randomization*
*note: R also stands for multiple correlation according to the textbook so keep this in mind
What is the formula for calculating gamma?
G = (A-D)/(A+D)
A= agreements/cases in predicted direction
D= disagreements/cases not in predicted direction
What four things should consumers of statistical findings pay attention to?
- statistical significance shouldn’t be taken as indicative of substantive significance
- beware of statistics of convenience or types of analyses that may be biased
- be wary of discussion and generalization that goes beyond the limited statistical findings
- readers should be vigilant regarding the misapplication of statistical techniques that don’t meet required assumptions
What is the ecological fallacy?
the error of assuming that relationships based on groups can be validly assumed to be true of individual correlations
