An independent sample Is one taken, without the the company or people in question being involved, In or obtaining it .
A related Sample is one that the same people who own the business , or hire people to evaluate it , keep taking the same sample from. the same place & do not expand their area of research .
An independent is preferable ! because you will get A more Honest answer.
A type II error, also known as a false negative, occurs when the test fails to reject a false null hypothesis. For example, if a null hypothesis states a patient is healthy, and the patient is in fact sick, but the test fails to reject the hypothesis, falsely suggesting that the patient is healthy. The rate of the type II error is denoted by the Greek letter beta (β) and related to the power of a test (which equals 1-β).
Type I error: the error of rejecting a null hypothesis when it is actually true. We are making a Type I error when we observe a difference when in truth there is none.
Cumulative Type I Error = 1 - 0.99^n (when the same outcome is evaluated n times). The Cumulative Type I error increases as n increases.
ANOVA requires independence while there are two different versions of the t-test depending on wheter the two samples are independent or paired (dependent). When comparing multiple means (>2) multiple pairwise comparisons would have a larger cumulative type I error than ANOVA. You can read more about it in Multiple t tests or ANOVA (analysis of variance)?
The F distribution is calculated based on a ratio of two chi-square distributions. As such, it can have different sets of degrees of freedom: one in the numerator, and one in the denominator. It is most commonly used in ANOVA or MANOVA tests. With the F distribution, you can determine the probability that a group of samples all came from the same population. Using ANOVA is much like using a t-test. First you find the critical value of F based on the degrees of freedom and alpha. Then you calculate the F statistic based on the samples. If F < F-crit, then there is no significant difference between the groups. If a significant result is found, a post-hoc test can be used to determine which of the groups contribute to the significant results.