Plots for Two Variables | Statistics Tutorial | MarinStatsLectures

MarinStatsLectures-R Programming & Statistics
1 Oct 201909:00
EducationalLearning
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TLDRThis script discusses various plots for visualizing relationships between different types of variables: categorical and numeric, two categorical, and two numeric. It explains side-by-side box plots for one categorical and one numeric variable, highlighting an example with skin cancer and sun exposure. For two categorical variables, it describes side-by-side bar charts, stacked bar charts, and mosaic plots, using smoking and lung cancer as an example. Finally, for two numeric variables, scatter plots are introduced, with age and height as an example. The script also briefly mentions analytical techniques like t-tests, ANOVA, chi-squared tests, and correlations for different variable types.

Takeaways
  • 📊 The video discusses various plots to visualize relationships between different types of variables: categorical and numeric, two categorical, and two numeric.
  • 🔍 For one categorical and one numeric variable, side-by-side box plots can be used to explore associations, such as the hours spent in the sun related to skin cancer.
  • 📈 Analytic techniques like two-sample t-tests and analysis of variance are applicable for analyzing relationships between one categorical and one numeric variable.
  • 🎯 When there's no association, as with biological sex and body temperature, side-by-side plots will show similar distributions.
  • 📊 For two categorical variables, side-by-side bar charts, stacked bar charts, and mosaic plots are effective in illustrating associations, such as the link between smoking and lung cancer.
  • 🔍 Chi-squared tests, Fisher's tests, and calculating odds ratios and rate ratios are methods used to analyze relationships between two categorical variables.
  • 📊 Mosaic plots are particularly useful as they convey additional information, such as the proportion of the sample that belongs to each category.
  • 🎯 A mosaic plot without association would form a cross pattern, indicating similar proportions across categories.
  • 📈 Scatter plots (XY plots) are used to visualize relationships between two numeric variables, showing trends or correlations, like age and height in children.
  • 🔍 For two numeric variables, analytic techniques include Pearson's or Spearman's correlation, and simple linear regression.
  • 📈 In adults, there's typically no association between age (20-65) and height, resulting in a scatter plot with no discernible pattern.
  • 👍 The video encourages viewers to subscribe for more content and provides a brief overview of various data visualization and analysis methods.
Q & A

  • What is the purpose of using plots to describe the relationship between variables?

    -The purpose of using plots is to visualize and explore whether or not two variables are associated and the nature of that association.

  • What are the two types of variables that can be analyzed with plots?

    -The two types of variables that can be analyzed with plots are categorical and numeric.

  • What is a side by side box plot and when is it used?

    -A side by side box plot is used to compare the distribution of a numeric variable across different categories of another categorical variable. It is used when there is one categorical and one numeric variable.

  • How can a side by side box plot reveal an association between variables?

    -A side by side box plot can reveal an association by showing differences in the distribution of the numeric variable among the categories of the categorical variable.

  • What are some plots that can be used to describe the relationship between two categorical variables?

    -Some plots that can be used for two categorical variables include side by side bar charts, stacked bar charts, and mosaic plots.

  • What does a mosaic plot add in terms of information compared to a stacked bar chart?

    -A mosaic plot adds the extra information of the proportion of the sample that belongs to each category of the categorical variable, which is shown by the width of the bars in the plot.

  • How does a scatter plot (XY plot) help in understanding the relationship between two numeric variables?

    -A scatter plot helps by displaying the individual data points and revealing patterns such as correlations, trends, or absence of association between the two numeric variables.

  • What statistical tests can be used to analyze the relationship between one categorical and one numeric variable?

    -Statistical tests for one categorical and one numeric variable include two sample t-tests and analysis of variance.

  • What are some analytical methods for examining the relationship between two categorical variables?

    -Analytical methods for two categorical variables include chi-squared tests, Fisher's exact tests, odds ratios, and rate ratios.

  • What types of analyses are appropriate for two numeric variables?

    -For two numeric variables, analyses such as Pearson's or Spearman's correlation, and simple linear regression can be used.

  • How does the distribution of body temperatures for males and females illustrate a lack of association?

    -If the distribution of body temperatures for males and females looks pretty similar, it suggests that there is no significant difference between the two groups, indicating a lack of association between biological sex and body temperature.

Outlines
00:00
📊 Exploring Relationships with Plots

This paragraph introduces the concept of using plots to visualize the relationship between two variables, one categorical and one numeric, and between two categorical variables. It emphasizes the importance of plots in understanding associations and provides an example of side by side box plots to illustrate the association between skin cancer and sun exposure. The paragraph also briefly mentions upcoming discussions on analytic techniques and the dependency of the type of plots and analysis methods on the variable types.

05:05
📈 Comparing Categorical Variables with Mosaic Plots

This paragraph delves into the details of comparing two categorical variables using different types of plots, such as side by side bar charts and stacked bar charts. It provides a detailed example using smoking habits and lung cancer incidence to demonstrate how these plots can reveal associations. The paragraph then introduces mosaic plots as a preferred method due to their ability to convey additional information about the proportion of the sample, as well as the association between variables. The example illustrates the difference between smokers and non-smokers in terms of lung cancer rates, and contrasts this with a scenario where no association is present.

Mindmap
Keywords
💡plots
In the context of the video, 'plots' refer to visual representations used to analyze and describe the relationship between variables. They are essential tools in data visualization, allowing viewers to understand complex data by showing trends, associations, or patterns. The video discusses various types of plots suitable for different combinations of categorical and numeric variables.
💡categorical variables
Categorical variables are data types that can be divided into groups or categories without a numerical order. These variables are used to classify observations into distinct groups based on characteristics such as 'yes' or 'no' for skin cancer, or 'male' or 'female' for biological sex. In the video, the relationship between categorical variables and numeric variables is explored through different plots.
💡numeric variables
Numeric variables consist of numerical values that can be measured and compared. They are often used to quantify data, such as a person's age, body temperature, or the number of hours spent in the Sun. The video discusses how numeric variables can be analyzed in relation to categorical variables through plots and statistical methods.
💡association
Association refers to the statistical relationship between two variables, indicating whether there is a connection or link between them. In the video, the concept of association is central to understanding the plots and their ability to reveal if and how variables are related. For instance, the video shows that there is an association between smoking and lung cancer.
💡side by side box plots
Side by side box plots are a type of data visualization that compares the distribution of two groups by placing their box plots next to each other. This plot is particularly useful for showing the median, quartiles, and the spread of data for each group, allowing for a quick comparison and the identification of any association between a categorical and a numeric variable.
💡stacked bar charts
A stacked bar chart is a variation of a bar chart where the bars are divided into segments, each representing a part of the whole. This type of chart is used to display the proportion of different categories within each group and can effectively show the relationship between two categorical variables, such as the association between smoking and lung cancer.
💡mosaic plots
Mosaic plots are a type of graphical display used to show the relationship between two categorical variables. They consist of a grid of squares where each square represents the count or proportion of observations in a particular category combination. Mosaic plots are particularly useful for displaying the association between variables in a clear and concise manner, as they can also show the marginal proportions of each variable.
💡scatter plots
A scatter plot, also known as an XY plot, is a graphical representation used to display values for two variables for a set of data. Each point on the plot represents the values of both variables for a single observation. Scatter plots are commonly used to identify correlations or trends between two numeric variables, such as the relationship between age and height.
💡chi-squared test
The chi-squared test is a statistical method used to determine if there is a significant association between two categorical variables. It compares the observed frequencies in each category with the frequencies expected under the assumption of no association. The test is mentioned in the video as one of the analytical techniques for analyzing the relationship between two categorical variables.
💡Pearson's correlation
Pearson's correlation coefficient is a statistical measure that quantifies the linear relationship between two numeric variables. It ranges from -1 to 1, with 1 indicating a perfect positive correlation, -1 indicating a perfect negative correlation, and 0 indicating no linear correlation. The video mentions Pearson's correlation as a method to analyze the relationship between two numeric variables.
💡analysis methods
Analysis methods refer to the various statistical techniques and procedures used to examine data and draw conclusions about relationships between variables. The video discusses different analysis methods suitable for different types of variables, such as two-sample t-tests for one categorical and one numeric variable, and chi-squared tests for two categorical variables.
Highlights

Overview of different plots for describing relationships between variables.

Importance of subscribing and enabling notifications for new videos.

Association between variables can be visualized through plots.

Analytic techniques for analyzing relationships between variables.

Categorical vs. numeric variables and their respective plots.

Side by side box plots for one categorical and one numeric variable.

Example of skin cancer and sun exposure hours.

No association example with biological sex and body temperature.

Side by side bar charts for two categorical variables.

Association example with smoking and lung cancer.

Stacked bar chart as an alternative to side by side bar charts.

Mosaic plot for additional information on associations.

Mosaic plot example with smoking, lung cancer, and sample proportions.

No association mosaic plot appearance.

Scatter plot (XY plot) for two numeric variables.

Association example with age and height in children.

No association in adults' age and height between 20 to 65.

Analytic methods for one categorical and one numeric: t-tests, ANOVA.

Analytic methods for two categorical: chi-squared, Fisher's test, odds ratios.

Analytic methods for two numeric: Pearson's, Spearman's correlation, regression.

Transcripts

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DataVisualizationStatisticalAnalysisCategoricalDataNumericalDataAssociationDetectionHealthResearchEducationalContentAnalyticalMethodsVisualizationTechniquesStatisticalPlots