Inferential Statistics

Inferential Statistics

Conducted to examine relationships, make predictions and determine differences among groups in studies (using our results from our sample and apply to population at large)

Considerations of Inferential Statistics

Study purpose, hypothesis, research question, level of measurement, design, number of groups studied

Four Key Factors of Inferential Statistics

Research question/hypothesis for the study, level of measurement of the dependent variables, number of groups studied, research design

Non-Parametric Study Design

Looking at differences/associations at the nominal or ordinal (not always) level or if they’re skewed/kurtotic

Parametric Study Design

Looking at differences/associations at the interval/ratio level

Independent Sample

Assignment of a subject to a group is unrelated to the assignment of other subjects

Paired Sample

Subjects selects for data collection are related in some way

Simple Linear Regression

1 independent variable predicting 1 dependent variable

Multiple Linear Regression

2+ independent variables predicting 1 dependent variable

Are Inferential Statistics quantitative or mixed methods?

Typically quantitative but can also be mixed methods

Pearson-Moment Correlation Coefficient

Looking for relationship/associations either using Pearson’s R or Spearman/Rho (nonparametric alternative) which is the most common correlation analysis at the interval/ratio level

Purpose of Pearson Correlation Coefficient 

Examine associations/relationships and doesn’t determine cause and effect

Positive (Direction) Relationship (Pearson Correlation Coefficient)

1 variable increases as the other variable increases OR 1 variable decreases as the other variable decreases

Negative (Inverse) Relationship (Pearson Correlation Coefficient)

1 variable increases as the other variable decreases

Effect Sizes of Pearson’s R

Weak: R < 0.3
Moderate: 0.3 < R < 0.5
Strong: R > 0.5

What do you need to determine Pearson’s R value?

Table of Critical Values, level of significance, degrees of freedom

Degrees of Freedom for Pearson’s R

(N-2)

How to find value of Mirror Image Table of Pearson R?

Look at the two variables you are trying to determine the relationship for and find the repeating value in the chart

What is the Pearson R value equal to?

Effect Size

What is the Effect Size of Pearson’s R used for?

Power analysis and to determine the sample size and examine the power of studies 

Smaller Effect Size Requires

Greater Sample Size Needed

Larger Effect Size Requires

Greater Sample Size Needed

Weak R Value Effect Size

<0.3 or > -0.3

Moderate R Value Effect Size

0.3 - 0.5 or -0.3 to -0.5

Strong R Value Effect Size

> 0.5 or < -0.5

Why is percentage of variance explained in a relationship calculated? 

To increase understanding about relationships between two variables for clinical significance 

The stronger the R, what does that indicate?

Greater the percentage of variance

Percentage of Variance Explained Formula

(R²) = ___ x 100