100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Statistics for Business $19.55   Add to cart

Summary

Summary Statistics for Business

 62 views  2 purchases
  • Course
  • Institution

This summary brings together all the information seen and discussed in statistics class, as well as my personal notes that helped me better understand the theory/exercises. I have included screenshots of calculations performed in Excel and highlighted or circled important numbers/figures in tables....

[Show more]

Preview 6 out of 113  pages

  • August 22, 2023
  • 113
  • 2022/2023
  • Summary
avatar-seller
Statisitcs
Contents
Language of data ..................................................................................................................................... 7
Stages in Quantitative Research.............................................................................................................. 7
Quantitative Research Question ............................................................................................................. 7
Quantitative vs. Qualitative research .................................................................................................. 7
Random experiment and variables ..................................................................................................... 7
Population ........................................................................................................................................... 8
Variables .............................................................................................................................................. 8
Classification of the variables .......................................................................................................... 9
Collect Data ........................................................................................................................................... 10
Population vs. Sample ....................................................................................................................... 10
Proper Sampling ................................................................................................................................ 10
Different Time Patterns ..................................................................................................................... 11
Data Matrix ........................................................................................................................................ 11
Descriptive Statistics ............................................................................................................................. 11
Qualitative Variables ......................................................................................................................... 11
Distribution of Outcomes: Frequency Analysis ............................................................................. 11
Summary Measures ....................................................................................................................... 12
Cumulative frequencies................................................................................................................. 12
Graphical Representation of Distribution of Outcomes ................................................................ 12
Quantitative Statistics ....................................................................................................................... 14
Distribution of outcomes and summary measures ....................................................................... 14
Distribution of Outcomes .............................................................................................................. 14
Discrete Variable (small number of outcomes)......................................................................... 14
Continuous variables or discrete with large number of outcomes ........................................... 15
Numerical Representation (Bins) .......................................................................................... 15
Graphical Representation...................................................................................................... 15
Summary Measures ....................................................................................................................... 17
Mean.......................................................................................................................................... 17
Variance and Standard Deviation .............................................................................................. 18
Skewness ................................................................................................................................... 19
Kurtosis ...................................................................................................................................... 19
Several measures for the center ............................................................................................... 19
Several measures for the spread ............................................................................................... 20
1

, Cumulative Distribution ................................................................................................................ 20
Interpretation ............................................................................................................................ 21
Interpolation.............................................................................................................................. 21
Quantile Function .......................................................................................................................... 22
Determining the kth- percentile with SPSS ................................................................................ 23
Quantiles to determine Summary Measures ............................................................................ 23
Distribution of Outcomes: BOXPLOT ..................................................................................... 24
Transformation of Data ................................................................................................................. 25
Logarithmic transformation ...................................................................................................... 25
Linear Transformation ............................................................................................................... 25
Summary Measures for Transformed Variables........................................................................ 25
Z-Score ....................................................................................................................................... 26
Binned Data ................................................................................................................................... 26
Cumulative Frequencies ............................................................................................................ 27
Interpolation for cumulative frequencies ............................................................................. 27
Percentiles ............................................................................................................................. 27
Summary Measures ................................................................................................................... 28
Relationships between variables....................................................................................................... 29
Distribution of combination of outcomes ..................................................................................... 29
Overview: Bivariate Descriptive Statistics ..................................................................................... 30
Relationships ................................................................................................................................. 31
Relationships between 2 Quantitative Variables .............................................................................. 31
Relationship between Quantitative and Qualitative Variables ......................................................... 33
Relationship between Quantitative Variables................................................................................... 33
Scatterplot ..................................................................................................................................... 33
Linear Association...................................................................................................................... 33
Covariance ................................................................................................................................. 34
Correlation................................................................................................................................. 34
Linear Combination of Variables ....................................................................................................... 35
Linear Transformation ................................................................................................................... 35
Linear Combination & Summary Measures .................................................................................. 36
Mean and variance for linear combinations ............................................................................. 36
Probability Theory ................................................................................................................................. 37
Definition ........................................................................................................................................... 37
Rules to determine probabilities ....................................................................................................... 37
Rule Laplace ................................................................................................................................... 37

2

, Counting Rules............................................................................................................................... 38
Axioms of Kolmogorov .................................................................................................................. 39
Conditional Probabilities ................................................................................................................... 40
General Multiplication Rule........................................................................................................... 40
Independence ................................................................................................................................ 41
Discrete Random Variables ............................................................................................................... 41
Random Variables.......................................................................................................................... 41
Probability Distribution for a Discrete Random Variable .............................................................. 42
Probability ..................................................................................................................................... 43
Cumulative Distribution ................................................................................................................ 43
Percentiles ..................................................................................................................................... 44
Summary Measures ....................................................................................................................... 44
Population Mean ....................................................................................................................... 44
Population Variance – Standard Deviation ............................................................................... 45
Binominal Distribution................................................................................................................... 45
Probability Distribution ............................................................................................................. 46
Expected Value (=Mean) and Variance ..................................................................................... 47
How the probability distribution looks like graphically............................................................. 47
Continuous Random Variable............................................................................................................ 47
Density ........................................................................................................................................... 47
Probability ..................................................................................................................................... 49
Cumulative Distribution ................................................................................................................ 49
Summary Measures ....................................................................................................................... 49
Continuous Distribution Models ................................................................................................... 51
Normal Distribution ................................................................................................................... 51
Parameter: ............................................................................................................................. 51
Probabilities:.......................................................................................................................... 51
Quantiles: .............................................................................................................................. 52
Normal Approximation: Normal Distribution for Binomial Distribution ................................... 52
Standard Normal Distribution ................................................................................................... 52
Linear Transformation & Combination for Discrete/continuous Random variables ........................ 54
Linear Transformation ................................................................................................................... 54
Linear critiions ............................................................................................................................... 54
Sums and Averages........................................................................................................................ 55
Expectation / Mean ................................................................................................................... 56
Variance ..................................................................................................................................... 56

3

, Distribution ................................................................................................................................ 57
Central Limit Theorem ................................................................................................................... 58
Conditions for applying the CLT ................................................................................................ 59
Foundation for Inference ...................................................................................................................... 60
Point Estimator .................................................................................................................................. 60
Confidence Interval ........................................................................................................................... 61
Ingredients..................................................................................................................................... 62
Determine the CI for mean µ ........................................................................................................ 62
Interpretation ................................................................................................................................ 63
Width of CI ..................................................................................................................................... 63
Assumptions .................................................................................................................................. 64
Basics of Hypothesis Tests ................................................................................................................. 64
All Steps ......................................................................................................................................... 65
Formulate hypotheses............................................................................................................... 65
Suitable Descriptive Statistics.................................................................................................... 66
P-value ....................................................................................................................................... 67
Conclusion ................................................................................................................................. 67
Assumptions .............................................................................................................................. 67
Two-Sided Test .......................................................................................................................... 67
Two-Sided Test with Confidence Intervals ............................................................................ 68
Right-Sided Test......................................................................................................................... 68
Critical Values and Power (Type 2 error)................................................................................... 68
Hypothesis Testing ................................................................................................................................ 70
H1Inference about means and correlations...................................................................................... 70
Hypothesis testing for one mean (sigma unknown)...................................................................... 70
Critical Value(s) ...................................................................................................................... 71
Confidence Interval ............................................................................................................... 72
SPSS ....................................................................................................................................... 72
Testing Normality .......................................................................................................................... 72
Kolmogorov-Smirnov test.......................................................................................................... 73
Shapiro-Wilk .............................................................................................................................. 75
Hypothesis testing to compare two means................................................................................... 75
Paired versus Unpaired ............................................................................................................. 75
Paired T-test → turns into t-test for one mean ........................................................................ 76
Confidence Interval ............................................................................................................... 77
Unpaired T-test → compares two means ................................................................................. 77

4

, (1) Test Statistics (known sigma): .......................................................................................... 78
(2) Test Statistics (unknown sigma):...................................................................................... 78
(3) Test statistic for (unknown) σ1= σ2:.................................................................................. 78
T-test to compare 2 means in SPSS ....................................................................................... 79
Confidence Intervals (unpaired means) ................................................................................ 79
Hypothesis Testing Compare More Than 2 Means – ANOVA ................................................... 80
Post-Hoc Test......................................................................................................................... 83
T-Test for Pearson Correlation .................................................................................................. 85
H2 Chi Square Test for goodness of Fit and Independence .............................................................. 87
Goodness Of Fit Test (Chi-Test) ..................................................................................................... 87
Independence (Chi Square Test) ................................................................................................... 90
5 Simple Linear Regression................................................................................................................ 93
SR_A Model Specification.............................................................................................................. 93
Assumptions .............................................................................................................................. 95
Nonlinear relationships ............................................................................................................. 96
Linear Model.......................................................................................................................... 98
Polynomial model: quadratic ................................................................................................ 98
Polynomial model: cubic ....................................................................................................... 98
Log transformation ................................................................................................................ 98
Log Linear Model ................................................................................................................... 99
Linear Log Model ................................................................................................................... 99
Log Log Model ....................................................................................................................... 99
Dummy Variable .................................................................................................................... 99
SR_B Inference about the regression parameters ...................................................................... 100
Fitted Model ............................................................................................................................ 100
Population vs. Estimated model .......................................................................................... 100
Least Squares Principles ...................................................................................................... 101
Residuals .............................................................................................................................. 101
Calculation LS (least squared) estimates ............................................................................. 102
Interpretation ...................................................................................................................... 102
Least Squares Prediction ..................................................................................................... 102
Estimate standard error of the model σ.............................................................................. 102
Properties of LSE...................................................................................................................... 103
Bi as a random variable ....................................................................................................... 103
Expected Value .................................................................................................................... 104
Variance ............................................................................................................................... 104

5

, Standard Error of the Parameters ....................................................................................... 104
Density ................................................................................................................................. 104
Gauss Markov theorem ....................................................................................................... 105
Interval estimation and hypothesis testing ............................................................................. 105
Confidence Interval for β1 ................................................................................................... 105
Hypothesis Testing .............................................................................................................. 106
SR_C Goodness of Fit ................................................................................................................... 108
Decomposition of variance and R-square ............................................................................... 108
Measuring Goodness of Fit.................................................................................................. 108
SR_D Checking Assumptions ....................................................................................................... 111
Assumption 1 ........................................................................................................................... 111
Assumption A2 ........................................................................................................................ 112
Assumption A3 ........................................................................................................................ 112
Assumption A4 ........................................................................................................................ 113
Assumption A5 ........................................................................................................................ 113




6

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

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

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

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 lsoler191. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $19.55. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

81989 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$19.55  2x  sold
  • (0)
  Add to cart