Fiche de révision : Fundamentals of Data Analysis Techniques

📋 Course Outline

1. Definition of Data Analysis
2. Exploratory and Inferential Statistics
3. Multidimensional Data Analysis
4. Descriptive and Explanatory Methods
5. Types of Data (Primary/Secondary)
6. Univariate Data Analysis
7. Quantitative Discrete Variables
8. Quantitative Continuous Variables
9. Qualitative Variables
10. Bivariate Data Analysis
11. Correlation and Dependence
12. Quantitative-Quantitative Relationships

📖 1. Definition of Data Analysis

🔑 Key Concepts & Definitions

• Data Analysis: "An ensemble of techniques to discover the structure, possibly complex, of a multi-dimensional data table and to translate it into a simpler, summarized structure, often graphically represented." (J-P. Fénelon)
• Exploratory Statistics: Methods aimed at describing and summarizing available data, especially when data are numerous.
• Inferential Statistics: Methods that interpret data as partial representations of an infinite population, assuming data are realizations of random variables governed by probability laws.
• Multidimensional Data Analysis: Techniques used to analyze data with multiple variables to uncover relationships and structures.
• Descriptive Methods: Methods that provide summarized or synthesized information about data.
• Explanatory Methods: Methods that reveal relationships between variables.
• Univariate Data Analysis: Analysis focused on a single variable to summarize and describe its characteristics.

📝 Essential Points

• Data analysis aims to discover the structure of complex, multi-dimensional data tables and to simplify or summarize this structure, often graphically.
• It has developed significantly since the 1950s, driven by advances in computer technology and data storage, and is now widely used across scientific and industrial fields.
• The main goal of exploratory statistics is to describe data, while inferential statistics makes predictions or generalizations based on data.
• Multidimensional data analysis involves techniques that handle multiple variables, categorized into descriptive (e.g., PCA, clustering) and explanatory (e.g., discriminant analysis, regression) methods.
• Descriptive methods provide a summarized view, whereas explanatory methods focus on uncovering relationships between variables.
• Univariate analysis concentrates on one variable at a time, providing measures such as mean, median, mode, variance, and graphical representations like histograms or boxplots.

💡 Key Takeaway

Data analysis encompasses a range of techniques designed to understand, simplify, and interpret complex multi-variable data, with methods tailored for description or explanation, depending on the objective.

📖 2. Exploratory and Inferential Statistics

🔑 Key Concepts & Definitions

• Bivariate Data Analysis: The analysis of two variables observed on the same individuals to study their relationship. It involves examining how two variables co-vary or relate to each other within a dataset.

• Correlation and Dependence: These concepts describe the degree of relationship or independence between two variables.

  • Correlation measures the strength and direction of a linear relationship between two numerical variables.
  • Dependence indicates whether the variation in one variable is related to the variation in another, implying that the variables are linked or associated.

• Quantitative-Quantitative Relationships: The specific analysis of relationships between two numerical variables, often using measures such as correlation or covariance to quantify the strength and nature of their association.

📖 3. Multidimensional Data Analysis

🔑 Key Concepts & Definitions

• Analysis of Data: A set of techniques aimed at discovering the structure of a multi-dimensional data table and translating it into a simpler, summarized form, often graphically represented (Fénelon).

• Multidimensional Data Analysis: The exploration of data involving multiple variables to uncover relationships, hierarchies, or structures within large datasets.

• Methods of Multidimensional Data Analysis:

  • Descriptive Methods: Provide summarized or synthesized information about the data.
  • Explanatory Methods: Detect relationships between variables.

• Objectives of Multidimensional Data Analysis:

  • Represent vast numerical data sets in a simplified, synthetic manner.
  • Facilitate decision-making by highlighting significant trends and hierarchies.
  • Extract and hierarchize main trends, eliminating marginal or random effects.

• Methods Descriptive:

  • Principal Component Analysis (ACP): Represents a cloud of points in a low-dimensional space based on correlations among variables.
  • Correspondence Analysis (AFC or ACM): Studies proximities between individuals described by multiple qualitative variables and their modalities.
  • Classification Methods (Clustering): Groups individuals into homogeneous classes using hierarchical or non-hierarchical techniques.

• Methods Explanatory and Predictive:

  • Discriminant Analysis (AFD): Predicts a qualitative variable using numerical variables, based on geometric space reduction.
  • Regression Models: Predict a dependent variable (qualitative or quantitative) through a linear combination of explanatory variables.

📝 Essential Points

• Multidimensional data analysis aims to discover structure in complex data tables with many variables.
• It is classified into descriptive methods (which summarize data) and explanatory methods (which reveal relationships).
• The choice of method depends on the nature of variables (nominal, ordinal, or scale).
• Techniques like ACP, AFC, and clustering help reduce dimensionality and identify patterns.
• Explanatory techniques like discriminant analysis and regression are used for prediction and understanding variable relationships.
• These methods have developed significantly since the 1950s, driven by advances in computing and data storage.
• They are widely used across scientific and industrial domains to manage large, varied datasets.

💡 Key Takeaway

Multidimensional data analysis employs various descriptive and explanatory techniques to simplify, visualize, and understand complex datasets with multiple variables, aiding effective decision-making.

📖 4. Descriptive and Explanatory Methods

🔑 Key Concepts & Definitions

• Statistical analysis (see source): A set of methods used to collect, organize, present, summarize, and analyze data from observations. It serves to discover structure within data and facilitate decision-making.

• Statistical exploration (see source): Techniques aimed at describing and summarizing data, especially when data are numerous, to reveal patterns and relationships.

• Statistical inference (see source): Techniques that interpret partial data as representing a larger population, assuming data are realizations of random variables governed by probability laws.

• Analysis of data (see source): A collection of techniques designed to uncover the structure of complex, multi-dimensional data tables, often simplifying data for better understanding, frequently through graphical representation.

• Multidimensional data analysis (see source): Methods that analyze data with multiple variables, aiming to represent large datasets succinctly, either through descriptive or explanatory approaches.

• Descriptive methods (see source): Techniques that provide summarized or synthesized information about data, often using measures of central tendency, dispersion, and graphical representations.

• Explanatory methods (see source): Techniques that identify and analyze relationships or dependencies between variables, such as correlations, regressions, or tests of association.

• Variables types (see source): The nature of variables influences analysis choice:

  • Quantitative variables: numerical data.
  • Qualitative variables: categorical data, either nominal or ordinal.

• Representation of data (see source): Graphical tools like histograms, bar charts, boxplots, scatter plots, and contingency tables used to visualize data.

📝 Essential Points

• Data analysis aims to discover the structure of data, often by simplifying complex tables into interpretable forms, frequently graphically.

• Techniques have evolved since the 1950s, driven by advances in computing and data storage, and are now widely used across scientific and industrial fields.

• Multidimensional analysis involves two main objectives:

  • Descriptive: providing summarized information.
  • Explanatory: revealing relationships between variables.

• Descriptive analysis includes univariate analysis for single variables, using measures like mean, median, mode, variance, and graphical representations (histograms, boxplots).

• Quantitative variables can be discrete (integer values) or continuous (any value within a range), with specific graphical tools:

  • Discrete: bar charts, cumulative diagrams.
  • Continuous: histograms, cumulative curves.

• Qualitative variables are represented with bar charts, pie charts, and contingency tables.

• Bivariate analysis studies the simultaneous behavior of two variables, exploring possible dependence or independence, often using tables, correlation, or tests like chi-square.

• Tests such as the chi-square test evaluate the independence of qualitative variables, while correlation coefficients measure the strength of relationships between quantitative variables.

• Comparing means between groups (e.g., t-test) assesses if differences are statistically significant.

💡 Key Takeaway

Descriptive and explanatory methods are essential tools in data analysis, enabling the summarization of data and the identification of relationships, which support informed decision-making in various fields.

📖 5. Types of Data (Primary/Secondary)

🔑 Key Concepts & Definitions

• Primary Data: Data created for the first time by the researcher through direct efforts and experience, specifically to address their research problem. Also known as first-hand data or raw data. Methods of collection include surveys, observations, questionnaires, interviews, and case studies.

• Secondary Data: Data that has already been collected and recorded by someone else for purposes unrelated to the current research problem. It is easily accessible and obtained from sources such as censuses, government publications, archives, reports, books, articles, and websites.

• Data according to nature:

  • Time Series Data: Observations of the values of one or more variables at different points in time (e.g., GDP over years).
  • Cross-Sectional Data: Data collected on multiple variables at a single point in time across different units (e.g., household income in different regions).
  • Panel Data: Data that combines both time series and cross-sectional dimensions, observing multiple units over multiple time periods (e.g., income of households over several years).

📝 Essential Points

• Primary data is specifically collected to solve a particular research problem, often through direct methods such as surveys or observations.
• Secondary data is pre-existing, collected for other purposes, and used to support or complement primary data.
• The type of data (primary or secondary) depends on the source of collection.
• Data can also be classified based on its nature:
  • Time series (values over time)
  • Cross-sectional (values at a specific point in time)
  • Panel data (combination of both dimensions)
• The choice between primary and secondary data depends on research needs, resource availability, and data accessibility.

💡 Key Takeaway

Understanding the origin and nature of data—whether primary or secondary, and whether it is time series, cross-sectional, or panel—is essential for selecting appropriate analysis methods and ensuring accurate interpretation of results.

📖 6. Univariate Data Analysis

🔑 Key Concepts & Definitions

• Univariate Data Analysis: Techniques used to analyze a single variable to summarize and describe its characteristics. It aims to provide a concise overview of the data's distribution, central tendency, and variability.

• Variable Quantitative Discrete: A variable that takes only integer values. Example: age (rounded to the year). Measures include median, mode, and mean, with graphical representations like bar diagrams and cumulative diagrams.

• Variable Quantitative Continuous: A variable that can take any value within a range, often represented by intervals. Example: surface area used in agriculture. Measures include median, mean, variance, and standard deviation, with histograms and cumulative curves as graphical tools.

• Variable Qualitative: Variables representing categories or characteristics, not numerical values. Examples: profession, social category. When ordered, called ordinal; otherwise, nominal.

• Measures of Central Tendency: Values that summarize a data set by indicating its center. Include:

  • Mode: The most frequent value.
  • Median: The middle value that divides the data into two equal halves.
  • Mean (Average): The sum of values divided by the number of observations.

• Measures of Dispersion: Values that describe the spread or variability within data. Include:

  • Variance: The average squared deviation from the mean.
  • Standard Deviation (Ecart-type): The square root of variance, indicating average deviation from the mean.

• Graphical Representations:

  • Histogram: Displays the distribution of a quantitative variable.
  • Boxplot (Boîte à moustaches): Summarizes a variable using five statistics (minimum, first quartile, median, third quartile, maximum).
  • Cumulative Curve: Shows the accumulation of data points across the range.

📝 Essential Points

• Univariate analysis focuses on one variable at a time, providing summaries such as measures of central tendency and dispersion.
• For discrete variables, graphical tools include bar diagrams and cumulative diagrams.
• For continuous variables, histograms and cumulative curves are used, with measures calculated based on class centers.
• Qualitative variables are summarized through frequency distributions and visualized with bar or pie charts.
• The choice of measures and graphical tools depends on the variable type (discrete, continuous, qualitative).
• The analysis helps identify the distribution shape, central value, and variability, facilitating understanding of the data's basic properties.

💡 Key Takeaway

Univariate data analysis provides essential summaries of a single variable, enabling a clear understanding of its distribution, central tendency, and variability, which are foundational for further statistical analysis.

📖 7. Quantitative Discrete Variables

🔑 Key Concepts & Definitions

• Quantitative Discrete Variable: A variable that takes only integer values, representing counts or whole numbers. Example: Age (rounded to the year) of employees.
• Measures of Central Tendency: Techniques used to summarize a series of observations with a representative value.
  • Mode: The value with the highest frequency in the data set.
  • Median: The middle value that divides the data into two equal halves.
  • Mean (Average): The sum of all values divided by the number of observations.
• Measures of Dispersion: Techniques to describe the variability or spread of data.
  • Variance: A measure of how much the data points differ from the mean.
  • Standard Deviation (Ecart-type): The square root of variance, indicating the average distance from the mean.
• Graphical Representation:
  • Diagramme en bâtons (Bar Chart): A chart showing frequency distribution of discrete data.
  • Diagramme cumulatif (Cumulative Diagram): A stepwise graph representing cumulative frequencies.

📝 Essential Points

• A variable quantitative discrète only takes integer values, such as counts or whole numbers.
• Measures of central tendency (mode, median, mean) help summarize the data with a single representative value.
• Measures of dispersion (variance, standard deviation) describe how spread out the data points are around the central value.
• Graphical representations like bar charts and cumulative diagrams are used to visualize the distribution of discrete variables.
• For discrete variables, the diagramme en bâtons and diagramme cumulatif are complementary and used for detailed data analysis.
• The median divides the data into two equal halves, useful when data are skewed or contain outliers.
• The mean is calculated by summing all values and dividing by the total number of observations.

💡 Key Takeaway

Quantitative discrete variables are count-based data that can be summarized using measures of central tendency and dispersion, with graphical tools like bar charts and cumulative diagrams aiding in their analysis.

📖 8. Quantitative Continuous Variables

🔑 Key Concepts & Definitions

• Quantitative Continuous Variables: Variables that can take any value within a range, with observations not being precise values but intervals or ranges. Example: Surface agricole utilisée (SAU) expressed in hectares.

• Measures of Central Tendency: Statistical tools used to summarize a data series with a single representative value.

  • Mode: The value with the highest frequency or effectif.
  • Median: The value that divides the series into two equal parts.
  • Mean (Moyenne Arithmétique): The average of the data series, calculated as the sum of all observations divided by the number of observations.

• Measures of Dispersion: Tools to describe the variability or spread of data.

  • Variance: A measure of the average squared deviation from the mean.
  • Écart Type (Standard Deviation): The square root of variance, indicating the average deviation from the mean.

📝 Essential Points

• Variable Type: Quantitative continuous variables are associated with observations that are intervals or ranges, not precise points.
• Graphical Representation:
  • Histogram: Shows the distribution of the variable, often with class centers for continuous data.
  • Courbe Cumulative (Cumulative Curve): Represents the cumulative frequency or distribution.
• Calculation of Measures:
  • For continuous variables, the mean, variance, and écart type are computed using class centers instead of individual observations.
• Representation:
  • The histogram and cumulative curve are the main graphical tools for visualizing continuous data.
• Example: Surface agricole utilisée (SAU) divided into classes, each representing a range of hectares.

💡 Key Takeaway

Quantitative continuous variables are characterized by measurements over intervals, with key statistical summaries including measures of central tendency and dispersion, visualized through histograms and cumulative curves to understand their distribution.

📖 9. Qualitative Variables

🔑 Key Concepts & Definitions

• Qualitative Variables: Characteristics that are not numerical but represent categories or attributes. They are also called categorical variables.
• Nominal Variables: A type of qualitative variable where categories have no inherent order (e.g., profession, gender).
• Ordinal Variables: A type of qualitative variable where categories have a natural order (e.g., educational level, ranking).
• Modalities: The different categories or values that a qualitative variable can take.
• Variable (statistic): A characteristic observed on the population or sample, which can be qualitative (categories) in this context.
• Representation of Qualitative Variables: Graphical tools such as diagrams in columns, bars, or sectors are used to visualize the distribution of modalities.

📝 Essential Points

• Qualitative variables are characterized by non-numeric categories called modalities.
• When modalities are naturally ordered, the variable is called ordinal; otherwise, it is nominal.
• Common graphical representations include column diagrams, bar diagrams, and sector diagrams.
• The analysis aims to study the distribution of modalities within the population or sample, often to detect patterns or relationships with other variables.
• In bidimensional analysis, qualitative variables can be studied for dependence or association, often using tests like the chi-square (χ²).
• The chi-square test compares observed frequencies in a contingency table to expected frequencies under the assumption of independence, to determine if there is a significant association between variables.
• The coefficient phi, contingency coefficient, and Cramér's V are measures used to quantify the strength of association between two qualitative variables.
• Dependence or independence of variables is assessed through statistical tests, with significance levels guiding conclusions about relationships.

💡 Key Takeaway

Qualitative variables categorize data into distinct groups, and their analysis focuses on understanding the distribution of categories and testing for associations or dependence between variables using graphical and statistical methods.

📖 10. Bivariate Data Analysis

🔑 Key Concepts & Definitions

• Bivariate Data Analysis: A statistical approach to study the simultaneous variation of two variables observed on the same individuals, aiming to identify potential relationships or associations.

• Distribution Conjointe (Joint Distribution): The presentation of the combined data of two variables across all observations, often displayed in a tableau à double entrée (contingency table).

• Dépendance (Dependence): A relationship where the variation in one variable influences or is related to the variation in another variable.

• Indépendance (Independence): A situation where two variables vary independently; knowing one provides no information about the other.

• Variables liées (Related Variables): Variables whose variations depend on each other.

• Variables indépendantes (Independent Variables): Variables that vary without influencing each other; the knowledge of one does not inform about the other.

• Test de Khi-deux (Chi-square Test): A statistical test used to determine if there is a significant association between two qualitative variables in a contingency table.

• Corrélation (Correlation): A measure of the strength and direction of the linear relationship between two quantitative variables.

• Covariance: A mathematical measure to evaluate the direction of variation between two quantitative variables.

• Nuage de points (Scatter Plot): A graphical representation of two quantitative variables to visualize their relationship.

• Coefficient φ (Phi coefficient): A measure of association for 2×2 tables, indicating the strength of the relationship between two binary variables.

• V de Cramer (Cramér's V): A normalized measure of association between two categorical variables, ranging from 0 (no association) to 1 (strong association).

• Rapport de corrélation (Correlation Ratio): An indicator measuring the strength of the relationship between a quantitative variable and a qualitative variable.

• Test t de Student: A statistical test comparing the means of two groups to determine if the difference is statistically significant.

📝 Essential Points

• Bivariate analysis involves studying the joint distribution of two variables to detect relationships or associations.

• The distribution conjointe is often summarized in a contingency table for qualitative variables, with tests like chi-square used to assess independence.

• For two quantitative variables, the correlation coefficient (Pearson's r) and covariance evaluate the strength and direction of linear relationships, visualized through scatter plots.

• The hypothesis testing framework (H0: variables are independent; H1: variables are related) guides the interpretation of statistical tests like chi-square, correlation, and t-tests.

• The choice of analysis method depends on the types of variables involved (qualitative vs. quantitative).

• Measures like φ and V de Cramer quantify the strength of association in categorical data, while the correlation ratio assesses relationships between qualitative and quantitative data.

💡 Key Takeaway

Bivariate data analysis explores the relationship between two variables, using graphical and statistical methods to determine whether they are associated or independent, facilitating understanding of their joint behavior.

📖 11. Correlation and Dependence

🔑 Key Concepts & Definitions

• Correlation: A statistical measure that evaluates the strength and direction of the linear relationship between two variables. It is used in the analysis of two variables quantitatively (see "Analyse bidimensionnelle: Cas de deux variables quantitatives"). The correlation coefficient (Pearson's r) quantifies this relationship, with positive values indicating direct correlation and negative values indicating inverse correlation.

• Dependence: A relationship where the variation of one variable is related to the variation of another. Variables are linked if the change in one influences or is associated with the change in the other (see "Variables liées"). Dependence implies that knowing the value of one variable provides information about the other.

• Independence: A situation where two variables vary independently, meaning the variation in one does not affect or provide information about the variation in the other (see "Variables indépendantes"). In statistical testing, independence is often tested using the chi-square test for qualitative variables.

• Covariance: A mathematical method to evaluate the direction of variation between two quantitative variables. It measures how two variables change together, indicating whether they tend to increase or decrease simultaneously.

• Test de corrélation de Pearson: A hypothesis test to determine if a significant linear relationship exists between two quantitative variables. The null hypothesis (H0) states that there is no correlation (ρ=0), while the alternative (H1) suggests a correlation exists (ρ≠0). The test involves calculating a correlation coefficient and associated p-value.

• Test de khi-deux (χ2): A statistical test used to measure the degree of dependence between two qualitative variables. It compares observed frequencies in a contingency table to expected frequencies under the assumption of independence. If the calculated χ2 exceeds the critical value, dependence is inferred.

• Coefficient phi (φ): A measure of association for 2×2 tables, representing the strength of relationship between two variables with two modalities. It is the square root of the χ2 statistic divided by the sample size, ranging from 0 (no association) to 1 (strong association).

• Coefficient de contingence: An indicator that measures the association between two qualitative variables, ranging from 0 (independent) to a maximum less than 1, depending on table size. It is used to compare association strength across tables of the same dimensions.

• V de Cramer: A normalized coefficient that measures the strength of association between two qualitative variables, applicable for tables larger than 2×2. It ranges from 0 to 1, with values ≥0.8 indicating a very strong association.

📝 Essential Points

• Correlation assesses the linear relationship between two numerical variables, often visualized with a scatter plot ("Nuage de points"). A strong linear pattern indicates high correlation, positive or negative.

• Dependence implies that the variation in one variable is related to the variation in another, which can be tested statistically (e.g., χ2 for qualitative variables, Pearson's r for quantitative variables).

• Variables are considered independent if the statistical tests (like χ2 or correlation tests) do not show significant dependence (p-value > 0.05). Conversely, a significant test (p-value < 0.05) indicates dependence.

• The strength of association is interpreted through coefficients like φ and V de Cramer, with higher values indicating stronger relationships.

• For qualitative-quantitative analysis, methods like boxplots and histograms help visualize differences in the quantitative variable across categories of the qualitative variable.

💡 Key Takeaway

Correlation and dependence describe the nature and strength of relationships between variables, with statistical tests like Pearson's r and chi-square used to determine if these relationships are significant, guiding the understanding of how variables interact in data analysis.

📖 12. Quantitative-Quantitative Relationships

🔑 Key Concepts & Definitions

• Correlation: A statistical measure that evaluates the strength and direction of the linear relationship between two variables. It is used in the context of analyzing the relationship between two quantitative variables (see "Analyse bidimensionnelle: Cas de deux variables quantitatives").
• Covariance: A mathematical method to assess the direction of variation between two quantitative variables, indicating whether they tend to increase or decrease together.
• Test de corrélation de Pearson: A hypothesis test used to determine if there is a significant linear relationship between two variables, with hypotheses:
  • H0: ρ=0 (no correlation)
  • H1: ρ≠0 (correlation exists)
• Nuage de points: A graphical representation (scatter plot) used to visualize the relationship between two quantitative variables, often revealing linearity or other patterns.
• Nuage très étiré / modérément étiré / arrondi: Descriptions of scatter plots indicating the strength and nature of the relationship:
  • Very elongated: strong linear relationship, positive correlation.
  • Moderately elongated: weaker linear relationship, possibly negative correlation.
  • Rounded: no apparent relation.
• Test de Pearson: Used to test the significance of the correlation coefficient; involves calculating a p-value to accept or reject the null hypothesis of no correlation.
• Coefficient phi: A measure used for 2×2 tables to assess association strength between two variables with two modalities; calculated as the square root of χ² divided by the sample size.
• Coefficient de contingence: An indicator of association between two variables, ranging from 0 (no association) to less than 1, depending on table size.
• V de Cramer: A normalized measure of association between two categorical variables, ranging from 0 to 1, with values ≥0.8 indicating a very strong association.
• Rapport de corrélation: A statistical indicator measuring the strength of the relationship between a quantitative variable and a qualitative variable, often visualized with boxplots or histograms.
• Test t de Student: A hypothesis test comparing the means of two groups to determine if the difference is statistically significant, based on the t-statistic and critical value.

📝 Essential Points

• The analysis of two quantitative variables involves assessing the correlation and covariance to understand their relationship.
• Graphical tools like nuage de points help visualize the linearity and direction of the relationship.
• The test de corrélation de Pearson evaluates the significance of the observed correlation coefficient, with a p-value guiding the decision to accept or reject the null hypothesis of no correlation.
• When variables are categorical, tests like chi-deux and measures like phi, coefficient de contingence, and V de Cramer quantify the strength and significance of association.
• For mixed types (quantitative and qualitative), boxplots and histograms are used to compare group means, and the rapport de corrélation measures the association strength.
• The test t compares group means to determine if differences are statistically significant, considering the sample means, standard deviations, and sizes.

💡 Key Takeaway

Analyzing the relationship between two quantitative variables involves measuring correlation and visualizing data through scatter plots, while significance tests like Pearson’s determine if the observed relationships are statistically meaningful.

📅 Key Dates

(Absent in provided content; no key dates to include)

📊 Synthesis Tables

⚠️ Common Pitfalls & Confusions

1. Confusing exploratory statistics with inferential statistics; the former describes data, the latter generalizes.
2. Misinterpreting correlation as causation in bivariate analysis.
3. Overlooking the importance of variable types (quantitative vs qualitative) in selecting analysis methods.
4. Assuming all multivariate techniques are suitable for all data types without considering their nature.
5. Confusing descriptive methods with explanatory methods; they serve different objectives.
6. Ignoring the development context of methods since the 1950s, especially the role of computational advances.
7. Misapplying PCA or AFC without understanding their assumptions and data requirements.

✅ Exam Checklist

• Define data analysis and distinguish between exploratory and inferential statistics, referencing Fénelon’s definition.
• Explain the purpose and techniques of univariate data analysis, including measures like mean, median, and graphical tools.
• Describe the differences between quantitative discrete and continuous variables.
• Clarify the nature of qualitative variables and their analysis.
• Understand bivariate data analysis, including the concepts of correlation and dependence.
• Differentiate between correlation and dependence, and their relevance in quantitative-quantitative relationships.
• Summarize the main methods of multidimensional data analysis, including PCA, AFC, clustering, discriminant analysis, and regression.
• Recognize the objectives of multidimensional analysis: data simplification, pattern detection, and decision support.
• Master the distinction between descriptive and explanatory methods, including their typical techniques and applications.
• Know the significance of variable types (nominal, ordinal, scale) in selecting analysis methods.
• Recall the historical development of data analysis techniques since the 1950s and the influence of computer technology.
• Understand the graphical representations used in data analysis: histograms, boxplots, scatter plots, contingency tables.
• Be familiar with key authors and their contributions, especially Fénelon’s definition of data analysis.