The F-test | F 检验

📚 The F-test | F 检验

In A-level statistics, the F-test is a hypothesis test used to compare two population variances. It helps decide whether two independent samples come from populations with the same spread, or whether an entire regression model has explanatory power.

在 A-level 统计学中，F 检验是一种用于比较两个总体方差的假设检验。它帮助我们判断两个独立样本是否来自具有相同离散程度的总体，或者判断整个回归模型是否具有解释能力。

1. What is the F-test? | 什么是 F 检验？

The F-test uses the ratio of two sample variances to test a claim about two population variances. The test statistic is named F after Sir Ronald Fisher, who developed the analysis of variance.

F 检验使用两个样本方差的比值来检验关于两个总体方差的论断。检验统计量以 Ronald Fisher 爵士的名字命名为 F，他创立了方差分析方法。

Unlike the normal or t distributions, the F distribution is positively skewed and only takes non-negative values.

与正态分布或 t 分布不同，F 分布是正偏态的，并且只取非负值。

2. When to use the F-test | 何时使用 F 检验

Use an F-test when you need to compare the variances of two independent random samples. A common application is checking the assumption of equal variances before a two-sample t-test.

当你需要比较两个独立随机样本的方差时，可以使用 F 检验。常见应用是在进行双样本 t 检验之前，检验方差相等的假设。

It is also used in regression ANOVA to test whether all slope coefficients are simultaneously zero.

它也用于回归方差分析中，检验所有斜率系数是否同时为零。

3. The F-distribution |

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