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T-value

As explained in Effective Data Analysis

A t-value is the test statistic from a t-test representing a standardized difference between means or between a sample mean and a hypothesized value.

A t-value is the statistic produced by a t-test. It expresses a difference relative to the variation in the data: either a difference between two sample means or a difference between one sample mean and a hypothesized value. Independent-samples and repeated-measures t-tests address different ways of collecting the two sets of observations. section 4.2.1

A larger t-value can indicate a larger difference, but the number alone does not establish statistical significance. Interpret it with the test’s degrees of freedom and a chosen significance threshold (alpha). Compare t-values from the same kind of test when useful; do not treat a t-value and an ANOVA F-value as interchangeable. section 4.2.1

Before acting on a result:

  • Check the assumptions behind the parametric test, including the distribution of the data, sample variances, and extreme outliers. If those checks cannot be done diligently, consider a non-parametric test. section 4.2.1
  • Consider sample size alongside statistical significance: increasing it can produce a significant result even when the difference between group means remains small. section 4.2.1
Table 4.1 Abbreviated t-distribution table showing that increasing the degrees of freedom has diminishing returns on the t-critical values at each alpha level (p-value threshold).
degrees of freedom
alpha level
0.1
0.05
0.01
0.005
0.001
10
1.81
2.23
3.17
3.58
4.59
20
1.72
2.09
2.85
3.15
3.85
30
1.70
2.04
2.75
3.03
3.65
40
1.68
2.02
2.70
2.97
3.55
50
1.68
2.01
2.68
2.94
3.50
60
1.67
2.00
2.66
2.91
3.46
70
1.67
1.99
2.65
2.90
3.44
80
1.66
1.99
2.64
2.89
3.42
90
1.66
1.99
2.63
2.88
3.40
100
1.66
1.98
2.63
2.87
3.39
150
1.66
1.98
2.61
2.85
3.36
200
1.65
1.97
2.60
2.84
3.34

The t-distribution table links degrees of freedom and alpha to critical values, showing why a t-value needs context before it is judged significant. section 4.2.1

Try changing the sample size

Calculate a recommended sample size with statsmodels’ TTestIndPower, generate two normally distributed samples with NumPy, then run scipy.stats.ttest_ind. Repeat at different sample sizes and alpha thresholds; compare the resulting t-values, p-values, and significance decisions. section 4.2.2

How Effective Data Analysis covers it

How deep it goes
Defines the statistic and develops its interpretation through degrees of freedom, alpha, assumptions, and sample-size effects.
Examples
Uses two groups’ test scores and an exercise that varies sample size and alpha for simulated normal samples.
What it assumes
Assumes familiarity with t-tests, degrees of freedom, and p-values while defining what the t-value represents.
What you can do after
Practice/perform an independent-samples t-test with scipy.stats.ttest_ind and interpret its result alongside sample size and a significance threshold.
How it connects
Connects t-tests to degrees of freedom, p-values, alpha, parametric assumptions, sample size, and ANOVA.
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Effective Data Analysis. The section links point to the parts of the book it draws on.