9.4
P値
P 値は、統計において最も重要な概念の 1 つです。
P 値は確率値を表します。 P 値は、帰無仮説が真である場合、ランダムに選択された別のサンプルからの結果が、指定されたサンプルから得られた結果と同じかそれ以上に極端になる確率です。
データから計算された大きな P 値は、帰無仮説が棄却されていない…
サンプル統計量(サンプル比率など)から検定統計量を計算する場合、その統計量は確率分布に配置できます。
検定統計量のこの値は、曲線の下の領域と他の領域を区別します。
分布の裾のこの領域はP値であり、Pは確率を表します。
帰無仮説が真であると仮定すると、計算された検定統計量、またはそれよりも高い値を、特定の分布の臨界領域で観測する可能性は常にあります。
P値は、偶然だけで臨界領域の検定統計値を取得する確率を提供します。
したがって、P値が所定の値(0.05など)よりも小さいことが観察された場合、帰無仮説は、観察された結果の可能性が非常に低く、帰無仮説に反する証拠がより強いことを示しているため、帰無仮説を棄却します。
P値は、仮説または検定統計量の値に応じて、右裾、左裾、または両方の裾で計算できます。
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Q1: What does P-value represent in hypothesis testing?
The P-value, or probability value, represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true. It measures the likelihood of obtaining sample results by chance alone. A smaller P-value indicates stronger evidence against the null hypothesis.
Q2: How do you use P-value to make decisions about the null hypothesis?
Compare the P-value to a predetermined significance level, typically 0.05. If the P-value is less than 0.05, reject the null hypothesis, indicating the observed outcome is highly unlikely under the null hypothesis. If the P-value is greater than 0.05, fail to reject the null hypothesis.
Q3: Where is the P-value located in a probability distribution?
The P-value is the area at the tail of the probability distribution, demarcated by the test statistic value. It can be calculated at the right tail, left tail, or both tails depending on the hypothesis and test statistic value. This tail area represents the probability of observing extreme results by chance.
Q4: What does a large P-value indicate about your hypothesis?
A large P-value indicates insufficient evidence to reject the null hypothesis. However, a large P-value does not mean the null hypothesis is true. It simply suggests the observed data is reasonably likely under the null hypothesis, so you fail to reject it rather than accept it.
Q5: Is P-value the same as the probability of rejecting the null hypothesis?
No. P-value is not the probability of rejecting the null hypothesis, nor is it a statistical error rate or sampling error. P-value also does not indicate a 95% chance that the observed difference is real. It specifically measures the probability of observing the test statistic under the assumption that the null hypothesis is true.
Q6: Why is 0.05 commonly used as the significance level for P-values?
The 0.05 significance level is a predetermined threshold convention in statistics. When P-value is less than 0.05, results are considered statistically significant, meaning the observed outcome is highly unlikely by chance alone. This threshold balances the need to detect real effects while controlling false positives.
Q7: What information does P-value NOT provide about hypotheses?
P-value does not convey information about the truth of the null or alternative hypotheses. It does not indicate whether the null hypothesis is true, nor does it measure the magnitude or practical importance of an effect. P-value is solely a measure of evidence strength against the null hypothesis based on sample data.