Understanding type 1 error and type 2 error
- Thread starter BHeng9611
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Type 2 error chart:
On the Right you have a distribution chart with a mean at zero, and it has a 5% significance level marked on it. This means that only 5% of the data falls to the left of the threshold for statistical significance.
Now, in the second diagram (left), you have another distribution overlapping the first one (say we shifted the distribution to left just for sake of explanation). However, this new distribution has its mean shifted to the left, let's say at -6. Because of this shift, the distribution in the second diagram has a larger shaded region on the left, indicating a higher level of significance compared to the first distribution. In other words, more of the data in the second distribution falls to the left of the significance threshold.
Now, here's how this relates to Type 2 error:
Type 2 error occurs when you fail to detect a true effect or difference. In this analogy, think of the true effect or difference as something that's present in both distributions but is more pronounced in the second distribution due to the mean shift. However, even though this effect is more pronounced, the critical threshold for statistical significance (5% level) remains the same as in the first distribution. This means that while there is a real effect in the data, the statistical test might not detect it in the second distribution because the threshold for significance hasn't been adjusted to account for the mean shift.
In other words, the Type 2 error occurs when the test fails to recognize the true effect in the second distribution as statistically significant, even though it is more evident, simply because the significance threshold wasn't adjusted for the mean shift. This illustrates the importance of choosing an appropriate significance level and considering the context of your data to avoid Type 2 errors when conducting statistical tests.
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