independent group

(noun)

A statistical group of random variables that has the same probability distribution as the others, and that are all mutually independent.

Related Terms

Examples of independent group in the following topics:

  • Introduction

    • Typically, one group is given aspirin and the other group is given a placebo.
    • The groups are classified either as independent or matched pairs.
    • Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
    • The parameters tested using independent groups are either population means or population proportions.
    • When using the TI-83+/TI-84 calculators, we do not need to separate two population means, independent groups, population variances unknown into large and small sample sizes.

  • Using Two Samples

    • Typically, one group is given aspirin and the other group is given a placebo.
    • The groups are classified either as independent or matched pairs.
    • Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
    • The parameters tested using independent groups are either population means or population proportions.
    • Distinguish between independent and matched pairs in terms of hypothesis tests comparing two groups.

  • Graphical diagnostics for an ANOVA analysis

    • There are three conditions we must check for an ANOVA analysis: all observations must be independent, the data in each group must be nearly normal, and the variance within each group must be approximately equal.
    • For processes and experiments, carefully consider whether the data may be independent (e.g. no pairing).
    • Sometimes in ANOVA there are so many groups or so few observations per group that checking normality for each group is not reasonable.
    • The last assumption is that the variance in the groups is about equal from one group to the next.
    • Independence is always important to an ANOVA analysis.

  • t-Test for Two Samples: Independent and Overlapping

    • The two sample t-test is used to compare the means of two independent samples.
    • Paired t-tests are a form of blocking, and have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership in the two groups being compared.
    • The independent samples t-test is used when two separate sets of independent and identically distributed samples are obtained, one from each of the two populations being compared.
    • For example, suppose we are evaluating the effect of a medical treatment, and we enroll 100 subjects into our study, then randomize 50 subjects to the treatment group and 50 subjects to the control group.
    • In this case, we have two independent samples and would use the unpaired form of the t-test .

  • Introduction to comparing many means with ANOVA

    • Sometimes we want to compare means across many groups.
    • H0: The mean outcome is the same across all groups.
    • Compare groups I, II, and III.
    • Now compare groups IV, V, and VI.
    • For instance, group V appears to have a higher mean than that of the other two groups.

  • Comparing Two Sample Averages

    • Student's t-test is used in order to compare two independent sample means.
    • If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances.
    • The independent samples t-test is used when two separate sets of independent and identically distributed samples are obtained, one from each of the two populations being compared.
    • We enroll 100 subjects into our study, then randomize 50 subjects to the treatment group and 50 subjects to the control group.
    • In this case, we have two independent samples and would use the unpaired form of the t-test.

  • Summary of Functions

    • X = the number of independent trials until the first success (count the failures and the first success)
    • X = the number of items from the group of interest that are in the chosen sample.
    • X may take on the values x= 0, 1, ..., up to the size of the group of interest.
    • r = the size of the group of interest (first group)

  • Hypergeometric (optional)

    • You are concerned with a group of interest, called the first group.
    • Each pick is not independent, since sampling is without replacement.
    • The size of the group of interest (first group) is 80.
    • The size of the second group is 100.
    • The group of interest (first group) is the defective group because the probability question asks for the probability of at most 2 defective VCRs.

  • Simulating the study

    • Now, suppose the bankers' decisions were independent of gender.
    • The randomization of files in this simulation is independent of the promotion decisions, which means any difference in the two fractions is entirely due to chance.
    • What is the difference in promotion rates between the two simulated groups in Table 1.45?
    • How does this compare to the observed 29.2% in the actual groups?
    • This difference due to chance is much smaller than the difference observed in the actual groups.

  • Test of Independence

    • A test of independence determines whether two factors are independent or not.
    • If A and B are independent then P(A AND B) = P(A)P(B).
    • In a volunteer group, adults 21 and older volunteer from one to nine hours each week to spend time with a disabled senior citizen.
    • " tell you this is a test of independence.
    • This means that the factors are not independent.