Please enable JavaScript.
Coggle requires JavaScript to display documents.
Quantitative Analysis: Inferential Statistics What can sample data tell…
Quantitative Analysis: Inferential Statistics
What can sample data tell us about a wider population?
Test a claim
Inferential statistics
use sample data to evaluate a claim about a population.
The null hypothesis, H₀,
usually states that there is no effect or relationship.
The alternative hypothesis, H₁,
states the effect or relationship being investigated.
Evidence may support rejecting H₀.
A statistical test does not prove H₁ with certainty because another sample could produce different evidence.
Weigh the evidence
The p value
describes how unusual the observed result, or a more extreme one, would be if H₀ were true.
The significance level, α,
is the decision cutoff chosen before testing. A common choice is .05.
If p < α, reject H₀.
Otherwise, there is insufficient evidence to reject it.
A Type I error
occurs when a true H₀ is rejected.
Statistical significance does not describe the size or practical importance of an effect.
Show uncertainty
A sampling distribution describes how a statistic would vary across repeated samples.
Standard error measures that sampling variability.
A confidence interval gives a range of values compatible with the estimate and its uncertainty.
A smaller standard error generally produces a more precise estimate.
A 95 percent confidence level refers to the long run performance of the interval method across repeated samples. It does not mean there is a 95 percent probability that a fixed population value lies in one particular calculated interval.
Model relationships
The general linear model
represents an outcome as a function of one or more predictors.
A regression line
describes an estimated relationship.
The slope
describes the estimated change in the outcome for a one unit change in a predictor, holding other included predictors constant.
The intercept
is the estimated outcome when the predictors equal zero.
The error term
accounts for the difference between an observed outcome and the model’s prediction.
A fitted relationship alone does not establish cause and effect.
The research design and other possible explanations still matter.
Compare two groups
A t-test
assesses whether two group means differ beyond what might be expected from sampling variability.
A one tailed test
evaluates a direction specified in advance. A two tailed test evaluates a difference in either direction.
The t-statistic
compares the difference between group means with the standard error of that difference.
A p-value
addresses evidence against H₀; an effect size addresses magnitude. Both help interpret the result.
A two-group t-test and a one-way ANOVA
can test the same difference in means.
Study joint effects
A factorial design
studies two or more factors.
A
main effect
describes a factor’s association with the outcome across levels of another factor.
An
interaction effect
means the effect of one factor depends on the level of another.
A meaningful interaction changes how main effects should be discussed.
The result should be explained in terms of the relevant factor combinations rather than one overall effect alone.
A two-way ANOVA
can test two factors and their interaction.
Choose the right model
Regression
estimates relationships between predictors and an outcome.
Dummy variables
represent categories using values such as 0 and 1.
Covariates
account for other measured influences on the outcome.
Model specification
means deciding which variables and relationships belong in the model.
Theory and the research question should guide that choice.
Selecting a model only because it fits one dataset risks a misleading explanation.
Multiple regression
uses multiple predictors.
Multivariate regression
concerns multiple outcomes.
Recognize other approaches
Factor analysis
looks for a smaller set of underlying factors that may explain patterns among many measured items.
Logistic regression
models the probability of a binary outcome.
Path analysis
examines a system of proposed directional relationships.
Time series analysis
examines values collected over time, including possible dependence between observations.
ANCOVA
compares groups while accounting for covariates.
MANOVA
examines multiple outcomes.