Summary
Summary of major statistics themes
- Course
- Institution
Summary of major statistics themes. Helped me to survive the course. Great introduction.
[Show more]
Seller
Follow
desireeschmid
Content preview
STATISTICS SUMMARYThe Big Picture Summary of
Statistics
Some basic math:
- Two negatives make a positive: −2 × −4 = 8
- A negative number multiplied by a positive one make a negative number: 2 × −4 = −8
- BODMAS
o This is an acronym for the order in which mathematical operations are performed. It
stands for Brackets, Order, Division, Multiplication, Addition, Subtraction and this is
the order in which you should carry out operations within an equation.
~1~
,STATISTICS SUMMARY
~2~
,STATISTICS SUMMARY
Table of Contents
1 The Very Basics...................................................................................................................................6
1.1 Independent and Dependent Variables.......................................................................................6
1.2 Levels of Measurements..............................................................................................................6
1.3 Analyzing Data.............................................................................................................................6
1.3.1 Frequency distributions........................................................................................................6
1.3.2 Center of Distribution...........................................................................................................8
1.3.3 Dispersion in a distribution...................................................................................................8
1.3.4 Probability.............................................................................................................................8
1.3.5 Fitting statistical models to the data.....................................................................................8
2 Statistical Models................................................................................................................................9
2.1 Linear Models..............................................................................................................................9
2.2 The Mean as Statistical Model.....................................................................................................9
2.3 Standard Error...........................................................................................................................11
2.4 Confidence Intervals..................................................................................................................11
2.5 Test statistics.............................................................................................................................12
2.6 One- and two-tailed tests..........................................................................................................12
2.7 Type 1 and Type 2 error.............................................................................................................13
2.8 Effect Sizes.................................................................................................................................13
2.9 Statistical power........................................................................................................................14
3 Exploring data with graphs...............................................................................................................14
3.1 Graphing Relationships: Scatterplot...........................................................................................14
3.2 Histograms.................................................................................................................................14
3.3 Boxplots.....................................................................................................................................14
3.4 Check for Outliers......................................................................................................................15
3.5 Density Plots..............................................................................................................................15
4 Exploring Assumptions......................................................................................................................15
4.1 Assumptions of parametric data................................................................................................16
4.2 The Assumption of Normality....................................................................................................16
4.3 Testing homogeneity of Variance..............................................................................................17
4.4 Correcting Problems in the Data................................................................................................18
5 Correlation........................................................................................................................................18
5.1 How do we measure relationships?...........................................................................................18
5.2 Standardization and the correlation coefficient.........................................................................19
~3~
, STATISTICS SUMMARY
5.3 Spearman’s correlation coefficient............................................................................................20
5.4 Partial and semi-partial correlation...........................................................................................20
6 Regression........................................................................................................................................20
6.1 Method of least squares............................................................................................................21
6.2 Assessing the goodness of fit.....................................................................................................22
6.3 Assessing individual predictors..................................................................................................24
6.4 Simple Regression Summary......................................................................................................24
6.5 Multiple Regression...................................................................................................................25
6.6 Methods of Regression..............................................................................................................25
6.7 Accuracy of Regression model...................................................................................................25
6.8 Categorical Regression and multiple regression........................................................................27
7 Comparing two means......................................................................................................................27
7.1 The T-Test..................................................................................................................................27
7.1.1 Rationale.............................................................................................................................28
7.1.2 Assumptions........................................................................................................................28
7.2 Independent T-Test....................................................................................................................28
7.3 Dependent T-Test......................................................................................................................30
8 One-way ANOVA...............................................................................................................................31
8.1 Inflated error rates.....................................................................................................................31
8.2 Interpreting F.............................................................................................................................31
8.3 ANOVA as regression.................................................................................................................32
8.4 Logic of the F-Ratio....................................................................................................................34
8.5 Total Sum of Squares.................................................................................................................35
8.6 Model Sum of Squares...............................................................................................................35
8.7 Residual Sum of Squares............................................................................................................36
8.8 Mean Squares............................................................................................................................37
8.9 The F-Ratio.................................................................................................................................37
8.10 Assumptions of ANOVA...........................................................................................................38
8.11 What’s after ANOVA?...............................................................................................................38
8.11.1 Planned contrasts.............................................................................................................39
8.11.2 Post-Hoc Procedures.........................................................................................................41
9 Analysis of Covariance (ANCOVA).....................................................................................................43
9.1 Assumptions..............................................................................................................................43
9.2 General Procedure for ANCOVA................................................................................................44
9.3 Calculating the effect size..........................................................................................................46
10 Two-way ANOVA.............................................................................................................................46
~4~
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller desireeschmid. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $10.16. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52355 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now