David Normando

A PowerPoint®-based guide to assist in choosing the suitable statistical test.

NOTE: This presentation has the main purpose to assist researchers and students in choosing the

appropriate statistical test for studies that examine one variable (Univariate). Some multivariates analyses are also included.

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If you have any suggestion, criticism, please contact the author by e-mail: davidnor@amazon.com.br

David Normando

What do you want to do? For an answer, click on the button

1) I want to assess whether my data have a Normal distribution

2) I want to compare groups (Looking for differences between samples)

3) I want to make correlation or regression analysis between variables.

4) I want to check the replicability of data (analysis of random and systematic error)

5) I would choose the appropriate graph to my data.

David Normando

Tests for Data Analysis Distribution- NormalityNormal distribution is requested when using continuos data and n<30Normal distribution is requested when using continuos data and n<30

You may choose the test according to sample size.

Use D’Agostino, Use D’Agostino, ifif n n≥≥1010

Use D’Agostino-Pearson, Use D’Agostino-Pearson, ifif nn≥≥2020

Use Lilliefors or Shapiro-Wilk, Use Lilliefors or Shapiro-Wilk, for anyfor any n value n value

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What kind of data you have? (Click on the button).

Nominal

Ordinal

NUMERICALNUMERICALContinuousContinuous

NonparametricCategorical data

Parametric(mean)

Ex: height / length / weight (Assuming a normal distribution on n>30)

Ex: Frequency: Yes / No Race Gender

Ex: Middle (1) / Moderate(2) Severe (3)

Comparing groups (samples)

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How to check Normality ?How to check Normality ?

David Normando

Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

How many groups (samples) do you have?

1

2

>2

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Are your samples paired or dependent?

No

Yes

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

Numerical Data (parametric) If the distribution is not Normal, skip to "Abnormal"

ABNORMAL

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Answer: one sample t test

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Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

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Answer: Independent t testor ANOVA.

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Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

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Answer: Paired t test or ANOVA for repeated measurements..

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Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

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Answer: Analysis of Variance (ANOVA)or MANOVA (Multiple Analysis of Variance), if you have >1 variable.

Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

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Ordinal Categorical Data (Nonparametric)

2

>2

How many groups (samples) do you have ?

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No

Yes

Ordinal Categorical Data (Nonparametric)

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

Are your samples paired or dependent?

David Normando

No

Yes

Ordinal Categorical Data (Nonparametric)

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

Are your samples paired or dependent?

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Answer: Mann-Whitney test

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Ordinal Categorical Data (Nonparametric)

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Answer: Wilcoxon (signed rank test) or Signal test.

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Ordinal Categorical Data (Nonparametric)

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Answer: Kruskal-Wallis’ Test

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Ordinal Categorical Data (Nonparametric)

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Answer: Friedman’s Test

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Ordinal Categorical Data (Nonparametric)

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Nominal Categorical Data (Nonparametric)

2

>2

How many groups (samples) do you have ?

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No

Yes

Nominal Categorical Data (Nonparametric)

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

Are your samples paired or dependent?

David Normando

No

Yes

Nominal Categorical Data (Nonparametric)

Not sure? If some of the cells in the contingency table give

values (expected) lower than 5.

Is there any expected value <5 ?

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No

Yes

Nominal Categorical Data (Nonparametric)

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

Are your samples paired or dependent?

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Answer: Chi-square (x²) test or Binomial Test, if using 2 samples and proportion (%)

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Nominal Categorical Data (Nonparametric)

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Answer: Cochran’s test (absolute or relative frequence: %)

Nominal Categorical Data (Nonparametric)

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Answer: McNemar’s test

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Nominal Categorical Data (Nonparametric)

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Answer: Exact Fisher’s test

Nominal Categorical Data (Nonparametric)

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Correlation or Regression Analysis

Ordinals

Numerical

Nominal

What kind of data you have? (Click on the button).

Ex: height / length / weight (Assuming a normal distribution)

Ex: Frequency: Yes / No Race Gender

Ex: Middle (1) / Moderate(2) Severe (3)

How to check Normality ?How to check Normality ?

NonparametricCategorical data

Parametric(mean)

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Numerical Data (parametric) If the distribution is not Normal,

skip to "Abnormal" ABNORMAL

How many variables do you have?

2

>2

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Answer: Pearson’s Correlation

Simple Linear Regression

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ABNORMAL

Correlation tests or regression analysis to Continuos data

If the distribution is not Normal, skip to "Abnormal"

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Answer: Pearson’s Correlation (parcial) or Canonical Correlation

Multiple Linear Regression

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ABNORMAL

NOTE: For Correlation all variables examined must have a Normal Distribution.For Linear Regression dependent variable must have a Normal Distribution

How to check Normality ?How to check Normality ?

Correlation tests or regression analysis to Continuos data

If the distribution is not Normal, skip to "Abnormal"

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Answer : Spearman or Kendal Correlation

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Correlation test to Ordinal data

(nonparametric)

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How many variables do you have?

2

>2

Correlation and Regression Analysisto Nominal data (nonparametric)

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Answer: Contingency coefficient C

Simple Logistic Regression

Correlation test to Nominal data

(nonparametric)

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Answer: Contingency coefficient C

Multiple Logistic Regression

Correlation test to Nominal data

(nonparametric)

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Replicability or Reproducibility (Systematic error)

OrdinalOrdinal

NumericalNumerical

NominalNominal

What kind of data you have? (Click on the button).

Ex: height / length / weight (Assuming a normal distribution)

Ex: Frequency: Yes / No Race Gender

Ex: Middle (1) / Moderate(2) Severe (3)

NonparametricCategorical data

Parametric(mean)

How to check Normality ?How to check Normality ?

David Normando

Answer: Parametric test for dependent data

Note: Intraclass correlation can be used, if you would like to check the association between 2 or more measurements.

Replicability or Reproducibility (Systematic error for numerical data)

2 samples2 samples >2 samples>2 samples

ABNORMAL

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For random or casual error , you may use TEM (technical error measurement):

D= difference between repeated measures n=number of individuals

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Answer: Weighted Kappa

Replicability or Reproducibility (Systematic error for ordinal data)

2 sample > 2 samples

NOTE: in case of an ordinal variable, nonparametric tests for paired or dependent data can also be used

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Answer: Kappa

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Replicability or Reproducibility (Systematic error for Nominal data)

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Nominal

Ordinal

NumericalParametric(mean)

Graph Selection

What kind of data you have? (Click on the button).

Ex: height / length / weight (Assuming a normal distribution)

Ex: Frequency: Yes / No Race Gender

Ex: Middle (1) / Moderate(2) Severe (3)

Back to beginningBack to beginning

NonparametricCategorical data

David Normando

Comparing Independent Samples

Making Data Correlation or regression

Comparing Dependent Samples (paired)

Graph Selection

Not sure? Not sure? Dependent Samples mean: Dependent Samples mean:

Before X After Before X After Left Side X Right Side Left Side X Right Side

T1 x T 2 x T3T1 x T 2 x T3

David Normando

BOX-PLOT - Comparing Groups.Continuous or Ordinal Data (Score)

This chart describes the measure of central tendency (MEAN for continuos data or MEDIAN for Ordinal This chart describes the measure of central tendency (MEAN for continuos data or MEDIAN for Ordinal data), measures of dispersion (Standard deviation for parametric data or interquartiles deviation for data), measures of dispersion (Standard deviation for parametric data or interquartiles deviation for

Ordinal data) and the whiskers (maximum and minimum values )Ordinal data) and the whiskers (maximum and minimum values )

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Outlier: an observation that Outlier: an observation that is numerically distantis numerically distantfrom the rest of the data. from the rest of the data.

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Line graph for longitudinal data

This chart describes the measure of central tendency (mean for Continuos data or median This chart describes the measure of central tendency (mean for Continuos data or median for Ordinal data) longitudinallyfor Ordinal data) longitudinally

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Graphic for Correlation Tests or Regression Analysis

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Bar/Column GraphicNominal data (frequency)

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