dependent samples

a sampling method where the individuals selected for one sample are used to determine the individuals in the second sample

independent samples

sampling method where an individual selected for one sample does not indicate which individual is to be in the second sample

the three requirements to test hypotheses regarding the difference of two means with dependent sampling

1. the sample is obtained using simple random sampling
2. the sample data are matched pairs
3. the differences are normally distributed with no outliers or the sample size is large

Is the following independent or dependent sampling? Why?

A researcher wishes to compare personality types of lawyers and non-lawyers. She obtains a random sample of 217 professionals of each category who take a personality inventory and determines each individual's personality type.

The sampling is independent because the individuals selected for one sample do not dictate which individuals are to be in a second sample.

Is the following an independent or dependent sample?

An educator wants to determine whether a new cirriculum significantly improves standardized test scores for students. She randomly divides 80 students into two groups. Group 1 is taught using the traditional curriculum, while group 2 is taught using the new cirriculum. At the end of the school year, both groups are given the standardized test and the mean scores are compared.

independent sampling

The following data represent the muzzle velocity of shells fired from a 155-mm gun. For each shell, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. 

obser.    1         2       3       4

A          790    795   780   785

B          798    793   789   784

Why are these matched-pairs data?

1. All the measurements came from rounds fired from the same gun.
2. The measurements (A and B) are taken by the same instrument.
3. Two measurements (A and B) are taken on the same round.
4. The same round was fired in every trial.

The following data represent the muzzle velocity of shells fired from a 155-mm gun. For each shell, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. 

obser.    1         2       3       4

A          790    795   780   785

B          798    793   789   784

Is there a difference in the  measurement of the muzzle velocity between device A and device B at a standard deviation of 0.01 level of significance?

Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normaly distributed with no outliers.

What is your conclusion regadring H₀?

Do not reject H₀

What are matched-pairs samples/data?

Are often referred to as dependent samples.

Dependent samples are when the individuals selected for one sample are used to determine the individuals in the second sample