independent

Examples of independent in the following topics:

• Independent Events

  • Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs.
  • For example, the outcomes of two roles of a fair die are independent events.
  • To show two events are independent, you must show only one of the above conditions.
  • If two events are NOT independent, then we say that they are dependent.
  • The events are considered to be dependent or not independent.

• Summary of Types of Hypothesis Tests

  • Populations are independent and population standard deviations are known (not likely).

• Independence

  • Two events are independent if any of the following are true:
  • The two selections are not independent.
  • When selecting cards with replacement, the selections are independent.
  • Consider a fair die role, which provides another example of independent events.
  • First, note that each coin flip is an independent event.

• Example: Test for Independence

  • The chi-square test for independence is used to determine the relationship between two variables of a sample.
  • In this context, independence means that the two factors are not related.
  • The null hypothesis is that the two variables are independent.
  • It is important to keep in mind that the chi-square test for independence only tests whether two variables are independent or not.
  • In the chi-square test for independence, the degrees of freedom are found as follows:

• t-Test for Two Samples: Independent and Overlapping

  • Two-sample t-tests for a difference in mean involve independent samples, paired samples, and overlapping samples.
  • The two sample t-test is used to compare the means of two independent samples.
  • Two-sample t-tests for a difference in mean involve independent samples, paired samples and overlapping samples.
  • 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.
  • In this case, we have two independent samples and would use the unpaired form of the t-test .

• Independence

  • Just as variables and observations can be independent, random processes can be independent, too.
  • Example 2.5 provides a basic example of two independent processes: rolling two dice.
  • This can be generalized to many independent processes.
  • What if there was also a blue die independent of the other two?
  • We say that two events A and B are independent if they satisfy Equation (2.29).

• Using Two Samples

  • 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.
  • In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means.
  • Distinguish between independent and matched pairs in terms of hypothesis tests comparing two groups.

• Test of Independence

  • A test of independence determines whether two factors are independent or not.
  • You first encountered the term independence in Chapter 3.
  • If A and B are independent then P(A AND B) = P(A)P(B).
  • " tell you this is a test of independence.
  • This means that the factors are not independent.

• Using the Model for Estimation and Prediction

  • Standard multiple regression involves several independent variables predicting the dependent variable.
  • In addition to telling us the predictive value of the overall model, standard multiple regression tells us how well each independent variable predicts the dependent variable, controlling for each of the other independent variables.
  • As mentioned, the significance levels given for each independent variable indicate whether that particular independent variable is a significant predictor of the dependent variable, over and above the other independent variables.
  • Because of this, an independent variable that is a significant predictor of a dependent variable in simple linear regression may not be significant in multiple regression (i.e., when other independent variables are added into the equation).
  • This could happen because the covariance that the first independent variable shares with the dependent variable could overlap with the covariance that is shared between the second independent variable and the dependent variable.

• Introduction

  • 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.