Stats Final Exam

hypothesis

a testable statement, derived from theory, that indicates a cause and effect between two concepts; must be a testable causal relationships

Cross tabs

a method used to analyze the relationship between two or more categorical variables by displaying their joint frequency distribution in a table format, allowing for the examination of different between groups

research hypothesis

a specific prediction about the expected outcome of a study, typically involving the relationship between variables and tested using statistical methods; can be non-directional

null hypothesis

a statement asserting that there is no significant effect or relationship between the variables being studied, serving as the default position that researchers aim to test against in hypothesis testing.

chi-square statistics

a statistical method used to determine if there is a significant association between categorical variables by comparing observed frequency counts to expected counts.

95% confidence interval

critical value at 0.05 means…

observed values

the actual data points collected during an experiment or study that are compared against expected values in statistical analyses.

expected values

the predicted frequency counts in statistical analyses that are used as a baseline to evaluate observed values.

degres of freedom

the number of independent values or quantities which can be assigned to a statistical distribution, typically calculated as the sample size minus one for a single sample (n-1 or n-2)

x² value must be at least as large of its critical value to reject the null

how to know if value is significant from a chi-square test

cannot describe the direction or the size of the relationship (small relationship with large sample size will be significant)

limitations of cross-tabs

bivariation correlation coefficient or Pearson’s correlation coefficient

r, measures the strength and direction of the relationship

covariation

the extent to which the values of two variables move toegether

covariance

a measure of how much two random variables change together, indicating the direction of their linear relationship.

covariance formula

positive covariance

as X increases (decreases), Y tends to increases (decrease)

negative covariance

as X increases (decreases), Y tends to decrease (increase), indicating an inverse relationship.

1

the correlation coefficient of a perfect positive correlation

-1

the correlation coefficient of a perfect negative correlation

0

the correlation coefficient when there is no relationship

False

True/False: Correlation is causal, not linear

difference of means

A statistical test that compares the average values of two groups to determine if they are significantly different from each other.

operational defintion

a set of instructions that describe how to measure the value of your concept in the empirical world

validity and reliability

operational definitions must have

validity

extent to which your instrument measures the concept of interest

reliability

the consistency of a measure across time, items, and observers.

systematic error

tendency to assign values that are too high or low (bias)

random error

equal likelihood of assigning too high and too low values

causal explanation

policy implications require…

causal inference

unknown causal relationship between two or more variables

descriptive inference

unknown fact about a single variable

• theory that expects X to affect Y

• evidence of correlation between X and Y

valid causal inference requires

correlation

the values of two variables tend to move togetherp

prediction

knowing the value of X helps us predict the future value of Y

causation

a change in the value of one concept tends to produce change in the value of another concept

deterministic causal relation

cause (X) is always present when outcome (Y) occurs

probabilistic causal relation

cause (X) usually present when outcome (Y) occurs; outcome occurs with some likelihood when the cause is presentbut not guaranteed.

theory

causal explanations

causal relationship

how and why change in the value of one concept influences the values of another concept

• co-variation: do values of X co-vary with the values of Y?

• credible casual mechanism: is it possible for X to cause Y?

• endogeneity/reverse causation: could Y cause X?

• spurious correlation: does a third variable, Z, influence both the values of X and Y

threats to causal inference

descriptive data

data that summarizes characteristics or features of a population or phenomenon without inferring causality.

mean

the sum of all scores divided by the number of scores

deviation

difference between an observed value and the mean

mode

the most common score; most frequent value (i.e. category) of a variable in a dataset

median

the middle score (or the mean of the two middle scores); when data are arranged from lowest to highest, median is the middle value

variance

the sum of the squared errors divided by the number of data points, minus one; tells us typically how much a data point differs from the mean (layman’s terms: how much the values in a group differ from the average and from each other)

standard deviation

the square root of the sample variance; (layman’s terms: how far, on average, the values are from the average value)

regression equation

coefficient estimates (slopes)

the values that represent the relationship between the independent and dependent variables in a regression model, indicating how much the dependent variable is expected to increase or decrease as the independent variable increases by one unit.

correlation coefficient formula

coefficient/standard error of the coefficient

formula for t-stats (from the coefficient correlation)

probability distribution

describes how likely different outcomes are