STAT 313 Last Day

Deadlines

  • Final revisions are due by Sunday at midnight
  • Final Project is due by Sunday at midnight

Deadline Extensions

You cannot request deadline extensions for the final version of your Final Project. The assignment portal closes at 11:59pm on Sunday. Do not ride the line.

Peer Review Session (45-minutes)

Structure of Final Projects

Findings

The results of each hypothesis test go directly below the test.


Theory-based Methods

Your decision & conclusion for your hypothesis test go directly below your ANOVA table.

Simulation-based Methods

Your decision & conclusion for your hypothesis test go directly below your permutation distribution and p-value.

Hypothesis Test Conclusions

Conclusions should be written in terms of the alternative hypothesis


Did you reject the null hypothesis?

Then you have evidence that at least one group has a different mean!

Did you fail to reject the null hypothesis?

Then you have insufficient evidence that at least one group has a different mean!

Model Validity

In this section you discuss the reliability of the p-values you obtained based on the model conditions.

  • Independence
    • within groups
    • between groups
  • Normality of the distributions for each group
  • Equal variance of the distributions for each group

Conditions for Each Test

Each one-way ANOVA test considers different groups. So, your conditions should be evaluated for each test separately.

Conditions are never met!

\(H_0\): the condition is met

\(H_A\): the condition is violated


Just like we never say “I accept the null hypothesis,” we never say a condition is “met.” Instead, we say there is no evidence that the condition is violated.

Study Limitations

This section summarizes your understanding of the foundational aspects of experimental design.

Based on the sampling method used, what larger population can you infer the results or your analysis onto?

  • What were the inclusion criteria of the observations?
  • How does that influence the population you can infer your findings onto?

Based on the design of the study, what type of statements can be made about the relationship between the explanatory and response variables?

  • Were the explanatory variables randomly assigned to control for confounding variables?
    • How does that influence what you can and cannot say about the relationships between the variables?

Overall Conclusions

Based on the results of your analysis what is your conclusion for the questions of interest? Connect your conclusion(s) to the relationships you saw in the visualizations you made and the results of your hypothesis tests.


Did you distributions look similar but your hypothesis test said at least one group was different?

Think about how sample size effects p-values!

Did you reject the null hypothesis for your one-way ANOVA?

Look back at your visualizations – which group(s) look the most different?

Did you fail to reject the null hypothesis for your one-way ANOVA?

Look back at your visualizations – do all of the groups look relatively similar?

Remedying Condition Violations

Do you have really skewed data?

Try using a log transformation!

Un-transformed Variances

unittype var
C 84.826493
I 80.783024
IP 5.729663
P 129.138547
R 59.096925
S 49.280157
SC 49.923399
NA 112.284569

Log Transformed Variances

unittype var
C 1.6978424
I 0.8788463
IP 0.8990321
P 1.5659500
R 1.3621461
S 2.1770549
SC 1.6514917
NA 0.7591942


What do you think? Did it work?

Final Presentations

Presentation Structure

You will give a 3-minute presentation on one aspect of your final project you found the most interesting. Notice, you need to pick one aspect, since your presentation is so short.

Here are some examples of what you could choose:

  • The relationships you saw in the visualizations
  • The design of the study
  • The model you found best represents the relationships between variables you selected

Presentation Slides

For your presentation you are allowed to make two slides:

  1. A title slide (make it fun!) with your name
  2. A content slide

Your slides must be submitted as a PDF.

Deadline for slides

Slides are due by 5pm the night before your final exam timeslot. If you do not submit slides by the deadline, you will not be allowed to present.

Some Closing Thoughts…

I hope you leave this class understanding…

  • Reproducibility is a foundational aspect to scientific research.

  • Data visualizations tell you a story, where statistical tests only tell you a summary.

  • Multiple regression and ANOVA are powerful tools to explore multivariate relationships.

  • A well thought out study is more powerful than any statistical analysis.

The Discipline of Statistics

The field of Statistics was developed to evaluate evidence obtained from data. Over the last century, the use of statistics has become embedded as a component of the scientific process for many disciplines.

“Significance, the new s-word, is overused and underdefined in the realm of connecting statistical results to the underlying science.” (Higgs, 2013)

“I advocate a simple solution: Replace the s-word with words describing what you actually mean by it.”

Foundational ideas taught in statistics courses were invented by:

  • Francis Galton
  • Karl Pearson
  • Ronald Fisher

Remember to give yourself praise!