Introduction to Inferential Statistics

Inferential Statistics

Make conclusions about a larger population of values by making measurements in a smaller sample

inferential stats uses

probability to make predictions

There is always some data that is the result of ___ alone!

chance

Parametric Stats

Groups of stats related to making distributional assumptions about a population

Assume that your data comes from a population that follows certain ____

distribution patterns

parametric stats are More powerful than non-parametric b/c we can more likely detect a ___ or difference in data

true relationship

Non-parametric Stats

Non-normal distributions of populations

e.g. skewed distributions in handedness (left vs. right)

extremely smal sample sizes

Non-parametric tests include:

Chi squared (X²) analysis

Wilcoxin-ranking

Overview of Using Inferential Statistics in Research

1.State the hypothesis (research and null)

2.Define significance level (α)

◦Determine cut-offs for whether or not something is significant

3.Determine if data meets assumptions for chosen test statistic

◦Normal distribution vs. non-normal

4.Compute the parameters (mean, SD)

5.Compute the test statistic and obtain p-value

◦Filling data into statistical equations and determine p-value

6.Determine if result is statistically significant and clearly state a conclusion

◦p-value determines the statistical significance

Research hypothesis (H_a)

◦Best guess answer to the research question

◦The expectation that is to be tested – “when you run the test, what do you expect to occur”

◦aka alternative hypothesis

Null hypothesis (H₀)

◦States that there will be no relationship or difference between variables of interest (independent and dependent variable)

◦Null hypothesis is the “no-effect” statement

If your research hypothesis is that there will be a difference between two groups, then the ____ is that there is no difference between the groups

null hypothesis

Statistically, you are always testing the ___ hypothesis

null

Non-directional

}No prediction of direction being higher or lower

Yes/no scenario

Directional

Measures the direction of variation of two variables

Serum cholesterol is not affected by ingesting eggs

null hypothesis

Serum cholesterol is increased after the ingestion of eggs

directional

Serum cholesterol is affected by the ingestion of eggs

non-directional

If data show that it is unlikely that chance is causing observed differences, then this is a ____

significant difference

Results of an analysis are unlikely to be due to chance means that

Results are statistically significant

Reject the null hypothesis (H₀)

Might accept the alternative hypothesis (H_a)

if there is No significant difference:

May not be enough evidence to reject the H₀

Does not necessarily mean that there is no true effect occurring; just means the data is too weak to substantiate the effect

P-Value

Probability value

A statistical measure used to determine the probability that an observed outcome is the result of chance

The lower the p-value, the more likely your intervention or treatment was causing ”___” between your variables

significant difference

Alpha-Levels (α)

Cutoff or threshold value that determines if the level of the p-value is going to be defined as “statistically significant”

The most common alpha level is

0.05

◦If p≤0.05 = ___

◦If p>0.05 = ___

◦If p≤0.05 = statistical significance!

◦If p>0.05 = no effect observed

Inferential statistics are common in hard-science research such as

◦Determine efficacy of a drug

◦Evaluate relationships between a gene mutation and disease

In the medical lab, inferential statistics are used for method validations like

◦Accuracy

◦Precision

◦Comparison of methods for accuracy/precision

◦Linearity