Introduction to descriptive statistics

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1 Introduction to descriptive statistics Illustrated with XLSTAT Jean Paul Maalouf linkedin.com/in/jean-paul-maalouf Oct. 12,

2 PLAN XLSTAT: who are we? Statistics: definition & categories Variables, individuals Describing one qualitative variable: mode, flat sorting, pie charts Describing the link between two qualitative variables: cross tabulation (contingency table) Describing one quantitative variable: mean, standard deviation, median, quartiles, box plots Describing the link between one quantitative variable & one qualitative variable: multiple box plots Describing the link between two quantitative variables: scatter plot 1 quantitative var. x 1 quantitative var. x 1 qualitative var. All the data in this class were made up unless otherwise specified 2

3 XLSTAT: Who are we? XLSTAT is a user-friendly statistical add-on software for Microsoft Excel 3

4 XLSTAT A growing software and team XLSTAT realizes its first sale on the Internet New version, VBA interface, C++ computations, 7 languages New products, new website, growing and dynamic team Thierry Fahmy develops a user-friendly solution for data analysis: XLSTAT is born 1996 The company Addinsoft is created 2006 New offers adapted to business needs 2015 XLSTAT 365 Cloud version of XLSTAT for Excel 365 4

5 XLSTAT in a few numbers 200+ statistical features General or field-oriented solutions 50k users Across the world. Companies, education, research 16 employees Always receptive to the needs of users 120k visits/month on the website Easy tutorials available in 5 languages 7 languages 400 downloads/day 5

6 Statistics: definition The science that deals with the collection, classification, analysis and interpretation of data... 6

7 Statistics: 4 categories 7

8 Statistics: 4 categories Oct. 19 Nov. 9 Nov. 30 Description Exploration Tests Modeling I want to I want to easily extract I want to accept / I want to understand summarize data information from a reject a very precise the way a phenomenon using simple large data set hypothesis assuming evolves according to a statistics or charts without necessarily error risks. (t tests, set of parameters. (mean, standard having a precise ANOVA, correlation (regression, ANOVA, deviation, boxplots...) question to answer. (PCA, AHC...) tests, chi-square...) ANCOVA...) 8

9 Variables, individuals 9

10 A couple of definitions... Variable An element that can take different values Qualitative variable A variable that cannot be quantified. Examples: socioprofessional category, geographical origin, type of licence, blood type.. Quantitative variable A variable that can be quantified. Examples: invoice amount, number of likes on Facebook, sugar concentration, height... Individual Elementary statistical unit. Can be described with variables. Examples: customers, surveyed people, patients, laboratory mice... 10

11 Individuals Data set : online shoe selling platform Variables 11

12 Describing a qualitative variable 12

13 Describing qualitative variables EXAMPLE: preferred brand variable, summary statistics Most frequent category Flat sorting 13

14 Describing qualitative variables EXAMPLE: preferred brand variable, pie charts 14

15 Describing the link between two qualitative variables Cross tabulation 15

16 Describing the link between preferred brand & Origin or Gender 16

17 Describing the link between preferred brand & Origin or Gender : cross tabulation (contingency table) Counts Percentages 17

18 Describing a quantitative variable 18

19 Describing quantitative variables EXAMPLE: shoe size variable, summary statistics Shoe Pointure size 19

20 Describing quantitative variables EXAMPLE: shoe size variable, summary statistics Measuring the center of the data Mean Median (middle point) Pointure Shoe size 20

21 Describing quantitative variables EXAMPLE: shoe size variable, summary statistics Measuring the center of the data Mean Median (middle point) Measuring the dispersion of data Standard deviation (mean of the arrows) Variance = Standard deviation² Pointure Shoe size 21

22 Describing quantitative variables EXAMPLE: shoe size variable, box plot Maximum Tukey limit 25% of data 50% of data 3rd quartile Mean Median 1 st quartile 25% of data 25% of data 25% of data 50% of data Tukey limit Minimum 22

23 Describing the link between one quantitative variable and one qualitative variable 23

24 Link between 1 quantitative & 1 qualitative var. EXAMPLE in marketing: invoice amount according to origin Origin (qualitative variable) Invoice amount (quantitative variable) 24

25 Describing quantitative variables EXAMPLE in sensory data analysis: summarizing global quality of 3 brands of chocolates (quality scores 0-10) 25

26 Describing quantitative variables EXAMPLE in biostatistics: petal length of 3 iris species (Fisher 1936) 26

27 Describing the link between 2 quantitative variables How about using a quantitative variable on the x axis instead of a qualitative variable? 27

28 Describing the link between two quantitative variables 28

29 Describing the link between 2 quantitative variables Scatter plot - Invoice amount decreases with time spent on the website. 29

30 Describing the link between 2 quantitative variables: coloration according to 1 qualitative variable Scatter plot - Invoice amount decreases with time spent on the website. - Plutonians spend more money on the website compared to others. - Martians and humans form a relatively homogeneous group

31 Imagine having the same kind of reasoning on a higher number of variables... Exploratory statistics! Next webinar : October 19,

32 In summary... Description Exploration Tests Modeling Description of datasets with 1 or 2 or 3 variables. May be used to look for hypotheses. Synthetic description of data sets with > 2 variables. May be used to look for hypotheses. I want to accept / reject a very precise hypothesis assuming error risks. (t tests, ANOVA, correlation tests, chi-square...) 32

33 Take home message Descriptive statistics: commonly used tools according to the situation 1 qual. variable Flat sorting, mode, pie charts 1 qual. variable x 1 qual. variable Cross tabulation (contingency table) 1 quant. variable Center (mean / median) ; dispersion (variance / std. deviation / quartiles) ; box plot 1 quant. variable x 1 quant. variable Scatter plot 1 quant. variable x 1 qual. variable Quantitative descriptive statistics per category of the qualitative variable; multiple box plot chart 1 quant. variable x 1 quant. variable x 1 qual. variable Scatter plot with points colored according to the categories of the qualitative variable 33

34 Thanks for attending! All the tools we saw are available in all XLSTAT solutions Survey time 34

Statistics 201 Summary of Tools and Techniques

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