10.3 Choosing Appropriate Analysis Techniques

Selecting the right statistical test is crucial for accurate data analysis in marketing research. It involves understanding your research question, assessing data characteristics, and choosing between parametric and non-parametric tests based on data distribution and measurement scales.

Once you've chosen a test, applying statistical analysis techniques is key. This includes univariate analysis for single variables, bivariate analysis for relationships between two variables, and multivariate analysis for multiple variables. Understanding significance testing, correlation, regression, and ANOVA is essential for interpreting results.

Selecting Appropriate Statistical Tests

Selection of statistical tests

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• Determine the research question and hypothesis
  • Identify the variables of interest such as dependent and independent variables
  • Specify the relationship between variables to examine differences, associations, or predictions
• Assess the characteristics of the data
  • Scale of measurement categorizes data as nominal (categories), ordinal (ranked), interval (equal intervals), or ratio (equal intervals with true zero)
  • Distribution of the data indicates if data is normally distributed (bell-shaped curve) or skewed (asymmetric)
  • Sample size and independence of observations ensure adequate data points and no influence between observations
• Choose the appropriate statistical test based on research question and data characteristics
  • Univariate tests for describing single variables calculate descriptive statistics (mean, median, mode, standard deviation)
  • Bivariate tests for examining relationships between two variables include t-test (comparing means), ANOVA (comparing means across groups), correlation (assessing relationships), and chi-square (examining associations between categories)
  • Multivariate tests for analyzing relationships among multiple variables encompass multiple regression (predicting outcomes), factor analysis (identifying underlying factors), and cluster analysis (grouping similar observations)

Parametric vs non-parametric tests

• Parametric tests
  • Assume data is normally distributed following a bell-shaped curve
  • Require interval or ratio scale data with equal intervals between values
  • Examples include t-test (comparing means), ANOVA (comparing means across groups), Pearson correlation (assessing linear relationships), and linear regression (predicting outcomes)
• Non-parametric tests
  • Do not assume normal distribution of data and can handle skewed or asymmetric distributions
  • Can be used with nominal (categories) or ordinal (ranked) scale data
  • Examples include Mann-Whitney U test (comparing medians between two groups), Kruskal-Wallis test (comparing medians across multiple groups), Spearman rank correlation (assessing monotonic relationships), and chi-square test (examining associations between categories)
• Assumptions of parametric tests
  • Normality assumes data follows a normal distribution with a symmetric bell-shaped curve
  • Homogeneity of variance assumes equal variances across groups or samples
  • Independence assumes observations are independent of each other with no influence between data points
• Assumptions of non-parametric tests
  • Randomness assumes samples are randomly selected from the population without bias
  • Independence assumes observations are independent of each other with no influence between data points

Applying Statistical Analysis Techniques

Analysis techniques for data

• Univariate analysis
  • Descriptive statistics summarize data with measures like mean (average), median (middle value), mode (most frequent value), and standard deviation (spread of data)
  • Frequency distributions and histograms visually represent the distribution of a single variable
  • Measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation) describe the typical values and spread of data
• Bivariate analysis
  • t-test compares means between two groups to assess differences (independent samples t-test) or changes (paired samples t-test)
  • ANOVA compares means among three or more groups to examine differences or effects of factors
  • Correlation measures the strength and direction of the relationship between two variables
    • Pearson correlation assesses linear relationships for interval or ratio data
    • Spearman rank correlation evaluates monotonic relationships for ordinal data
  • Chi-square test assesses the association or independence between two categorical variables in a contingency table
• Multivariate analysis
  • Multiple regression predicts the value of a dependent variable based on multiple independent variables using an equation with coefficients
  • Factor analysis identifies underlying factors or latent variables that explain the variance and covariance among a set of observed variables
  • Cluster analysis groups observations or cases based on their similarity across multiple variables to identify homogeneous subgroups

Types of statistical analyses

• Significance testing
  • Null hypothesis ($H_0$) states no effect or difference, while alternative hypothesis ($H_a$) suggests an effect or difference
  • p-value represents the probability of obtaining the observed results or more extreme results if the null hypothesis is true
  • Significance level ($\alpha$) sets the threshold for rejecting the null hypothesis, commonly 0.05 for a 5% chance of Type I error (false positive)
  • Reject $H_0$ if p-value < $\alpha$, indicating significant results, or fail to reject $H_0$ if p-value ≥ $\alpha$, suggesting non-significant results
• Correlation
  • Pearson correlation coefficient ($r$) measures the strength and direction of the linear relationship between two continuous variables
    • Range: -1 ≤ $r$ ≤ 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation
    • Interpretation: $r$ = 0 (no correlation), $r$ > 0 (positive correlation, as one variable increases, the other tends to increase), $r$ < 0 (negative correlation, as one variable increases, the other tends to decrease)
  • Spearman rank correlation coefficient ($\rho$) is a non-parametric measure of the monotonic relationship between two variables, assessing the strength and direction of the relationship without assuming linearity
• Regression
  • Simple linear regression models the relationship between a dependent variable ($y$) and a single independent variable ($x$) using the equation: $y = \beta_0 + \beta_1x + \epsilon$
    • $y$: Dependent variable or outcome variable being predicted
    • $x$: Independent variable or predictor variable used to predict $y$
    • $\beta_0$: Intercept or constant term, representing the value of $y$ when $x$ is zero
    • $\beta_1$: Slope or regression coefficient, indicating the change in $y$ for a one-unit change in $x$
    • $\epsilon$: Error term or residual, representing the unexplained variation in $y$
  • Multiple regression extends simple regression to include multiple independent variables ($x_1, x_2, ..., x_k$) to predict a dependent variable ($y$) using the equation: $y = \beta_0 + \beta_1x_1 + \beta_2x_2 + ... + \beta_kx_k + \epsilon$
    • $x_1, x_2, ..., x_k$: Independent variables or predictor variables used to predict $y$
    • $\beta_1, \beta_2, ..., \beta_k$: Regression coefficients indicating the change in $y$ for a one-unit change in the corresponding independent variable, holding other variables constant
• ANOVA (Analysis of Variance)
  • One-way ANOVA compares means across three or more groups for a single independent variable (factor) to assess differences
    • F-test evaluates the overall significance of the model by comparing the variance between groups to the variance within groups
    • Post-hoc tests, such as Tukey's HSD (Honestly Significant Difference), conduct pairwise comparisons between group means to identify specific differences
  • Two-way ANOVA examines the effects of two independent variables (factors) on a dependent variable, considering both main effects and interactions
    • Main effects represent the impact of each independent variable on the dependent variable, ignoring the other independent variable
    • Interaction effect assesses the combined effect of the independent variables on the dependent variable, indicating if the effect of one variable depends on the level of the other variable