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A one-tailed test is employed when you have a clear hypothesis about the direction of an effect. Imagine if you're predicting a new drug will lower blood pressure by a certain degree. You are not interested if it increases it or if there's no change.
In essence, you focus only on one side of a distribution curve, either more or less but not both.
The advantage here is that by concentrating on only one tail, you have more power to detect an effect. This increase in power can be useful in scientific studies where a predicted direction is hypothesized.
For example:

• Testing if a new marketing strategy increases sales compared to the old one.
• Determining if changing classroom lighting lowers error rates for students.

A two-tailed test is used when you are simply interested in finding out if there is any difference at all, not limited to a specific direction.
In other words, this test allows for the possibility that your effect could occur in either direction, either greater or lesser.
This involves splitting your significance level between both ends of the distribution. Such a test is necessary when you want to remain open to both possibilities without bias towards an expected outcome.
Examples of when you might use this include:

• Determining if a new training program has a different effect on employee performance, positive or negative.
• Testing whether a revised medication influences patient symptoms differently compared to the original medication.

Statistical power is the probability that a test will correctly reject a false null hypothesis. In simpler terms, it's a measure of a test's ability to detect an effect if there is one.
High statistical power reduces the likelihood of making a Type II error, which is failing to detect an effect that is present.
Statistical power can be influenced by:

• The significance level (alpha): Lower significance levels reduce power.
• Sample size: Larger samples can increase power.
• Effect size: A larger effect is easier to detect and thus increases power.

In practice, ensuring high statistical power is crucial for making confident decisions based on your test results.

A Type I error occurs when the test results lead you to incorrectly reject the null hypothesis when it is actually true.
This is also known as a 'false positive'. Imagine concluding that a new drug works when, in fact, it doesn't.
The probability of making a Type I error is denoted by the significance level (alpha).
So, if your alpha is set at 0.05, there's a 5% chance of a Type I error occurring.
It's critical to determine the balance between avoiding Type I errors and having enough power to detect actual effects.

The significance level, often denoted as alpha, is a threshold for determining when to reject the null hypothesis.
It's traditionally set at 0.05, meaning you would reject the null hypothesis if there's a 5% or less probability that the observed data could occur under the null hypothesis.
Choosing a suitable significance level is crucial, as it impacts the likelihood of committing Type I errors.
A lower significance level reduces the chance of such errors but also lowers the test power. Therefore, it's a balance to strike based on how much evidence you require before drawing a conclusion from your data.
Always adjust your significance level in accordance to the context of your research or decision-making considerations.