Welcome back to the AI Bayeslab Statistics series. I recognize you have access to a wealth of data in your role. With the AI Agent online tool, Bayeslab, you will find that almost 90% of your data analysis tasks can be managed independently, removing the necessity for a specialized data analyst.
We introduced a visualization chart type named “Estimation Plot” in the template Column Table — Paired t-test.
Today, let’s proceed with the basic statistical methodology. We will begin by defining specific paired data and discussing the characteristics of the paired data table structure. In the upcoming article, we will further examine the t-test for correlated or paired data samples.
1.What is paired data? Independent groups VS Correlated groups
Let's explore the definition of independent groups and correlated groups first.
Independent groups: Each sample in the data set is unique; removing any individual from the set will not affect the other individuals in the groups.
Correlated groups: Data is collected when effects are observed among individuals, indicating a one-to-one correspondence.
2.How to know if data is paired or independent
To determine if data are paired or unpaired, consider the following questions:
Origin of Data Points:
Are the data points obtained from the same source or from an individual? If so, this indicates paired data.
For instance, measuring the same individual multiple times (before and after treatment) yields paired data.
One-to-One Correspondence:
Do the data points in one set correspond directly to specific points in another set? If every observation in one group has a specific match in the other group, the data is considered paired.
Independence of Observations:
Data is deemed independent if removing a data point from one group does not affect the other group. This occurs when observations come from individuals or groups with no inherent connections.
3.Data Sample: Paired data vs Unpaired data
Here's an example for independent and correlated groups:
Independent Groups:
You choose students from two separate schools and assess their math scores. Each school's sample is independent, meaning the data from one does not influence the other.
School A scores: [85, 90, 78, 92]
School B scores: [88, 76, 95, 89]
Correlated Groups:
You give a midterm and final exam to the same students at one school and track their scores for both assessments. Each student's midterm and final scores are linked since they are from the same person.
Note: If you remove a student's data in correlated groups, you must remove both their midterm and final exam scores.
Midterm scores: [85, 90, 78, 92]
Final exam scores: [87, 88, 80, 95]
4.How to plot paired data in Excel?
Typically, we can visualize the data using a column or a grouped table. What are the characteristics of a column table?
4.1 Column
One column of data = one group
No grouping across rows. You are free to rearrange each row without affecting the data analysis.
There are two types of tables for columns,
Type 1: single column, that means each column or field represents a set of samples
Note： This type cannot plot paired data; only type 2 below is appropriate.
Type 2: Paired or Repeated Measures Input: each row in column one has an associated title.
4.2 Grouped table
What are the characteristics of a grouped table?
Each column = one group
Each row = another group
There are two types of tables for grouped tables,
Type 1: Enter and plot a single Y value for each point
Type 2: n replicate values in side-by-side sub columns
5.Visualization diff: Paired data vs unpaired data
And the visualization of paired data as above, we will not discuss the details of the achievement process here, as we will address it in the next post. That's all the content we discussed today. Stay tuned, subscribe to Bayeslab, and help everyone gain mastery in the wisdom of statistics affordably.
AI prompts serve as potent tools that help us efficiently complete various tasks and achieve desired outcomes. By utilizing technology in this manner, I believe we have a remarkable opportunity to reintroduce statistics into everyday life, reigniting interest in data and fostering analytical thinking.
Reviving this is crucial as statistics offer significant insights into different life aspects, aiding individuals in making better-informed choices. By ensuring statistics are accessible and pertinent, we improve comprehension and enable individuals to interact meaningfully with data, ultimately enhancing their daily lives.
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