Master Paired t-Tests

By Learn Statistics Easily

What is a Paired t-Test?

[{"selector":"#anim-88d38ee3-ecad-4369-9954-c79752c4b8ee [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] A statistical method comparing means of two related groups to reveal truths.

Key Assumptions

[{"selector":"#anim-f47344cb-845d-4795-96ec-448e3fc195ee [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Data must be paired, differences normally distributed, observations independent.

Formula Breakdown

[{"selector":"#anim-776672d5-1c37-4ca9-9dc5-f893ed37b511 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] t = d / (sd / √n), where d is mean difference, sd is standard deviation, n is pairs.

Calculating Differences

[{"selector":"#anim-bf5694ca-2e06-49da-a6b0-4469b9ba5376 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Subtract 'Before Treatment' from 'After Treatment' scores for each subject.

Descriptive Analysis

[{"selector":"#anim-2fe825a9-eb64-468a-9ab3-9678cde72caf [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Analyze the mean and standard deviation of the differences to understand variability.

Conduct the Test

[{"selector":"#anim-ba6d1360-e54b-4a77-b476-86838b11537e [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Use the formula with your calculated mean difference, sd, and number of pairs.

Visualize Changes

[{"selector":"#anim-89a4a017-4350-4398-84b6-ef883a47e0ec [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Graph before and after scores with lines connecting pairs to see treatment effect.

Interpret Results

[{"selector":"#anim-6154cd4f-9da1-401a-abd9-1442b5251a0a [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] A significant p-value (<0.05) indicates a meaningful difference due to treatment.

Using R Software

[{"selector":"#anim-397c5130-2cc1-4352-bcdb-142d69e3b508 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Leverage R's 't.test()' function for efficient paired t-test calculations.

Effect Size Matters

[{"selector":"#anim-5f13918c-7809-48c2-96dd-9dc96c15a5f3 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Beyond p-value, assess effect size with Cohen's d to gauge treatment impact.

Applications

[{"selector":"#anim-86ffa881-cf05-43cc-aa27-60c0d8a17f1e [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Paired t-tests are crucial in medicine, marketing, education, and more.

Ethical Implications

[{"selector":"#anim-87704a12-9b91-4828-a2ee-1ce6fb82f599 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Use paired t-tests responsibly to contribute to the common good.

Further Learning

[{"selector":"#anim-c74c7c62-0117-4667-a6d6-b2435f316860 [data-leaf-element=\"true\"]","keyframes":{"transform":["translate(-1.0302869668521453e-13%, 0%) scale(1.5)","translate(0%, 0%) scale(1)"]},"delay":0,"duration":2000,"easing":"cubic-bezier(.3,0,.55,1)","fill":"forwards"}] Ready to master paired t-tests? Click for a deep dive into advanced concepts!