Independence and Dependence Stats

If the conditional distribution of one variable is the same for each category of the other

• Association

• Independence

• Dependence

• Correlation

This table displays counts and percentages of individuals falling into named categories on two or more variables

• Frequency table

• Relative Frequency table

• Contingency table

• Data table

If events A and B are conditionally independent, what does it mean?

• The occurrence of event A increases the probability of event B happening, given some other event or condition.

• The occurrence of event A decreases the probability of event B happening, given some other event or condition.

• The occurrence of event A has no effect on the probability of event B happening, regardless of any other event or condition.

• The occurrence or non-occurrence of event A does not affect the probability of event B happening, given some other event or condition.

What is conditional independence in statistics?

• Two random variables are conditionally independent given a third variable if the conditional probability distribution of one variable given the other is equal to the conditional probability distribution of the variable given only the third variable.

• Two random variables are conditionally independent given a third variable if the conditional probability distribution of one variable given the other and the third variable is equal to the conditional probability distribution of the variable given only the third variable.

• Conditional independence in statistics means that the occurrence of one event does not affect the probability of another event happening.

• Conditional independence in statistics refers to the situation where two random variables are independent of each other.

If two events A and B are INDEPENDENT....

• the result of A happening DOES NOT change the probability of B occuring

• A and B have the same chance of happening

• If A happens, B will also happen

• the result of A happening will change the probability of B occuring

Use the probabilities in the Venn Diagram to determine if the events A and B are independent.

• A and B are independent because (0.25)(0.6) = 0.15.

• A and B are not independent because (0.25)(0.6) = 0.15.

• A and B are not indepedent because (0.4)(0.75) = 0.3 not 0.15.

• A and B are indepedent because (0.4)(0.75) = 0.3 not 0.15.

A random survey of 131 high school students was conducted on April 25. The results are shown in the table. Let A = being male and B = have completed ALL DLD assignments for 5 weeks. Are the events independent? Explain.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26

  P(A) x P(B) = 0.26 Since P(A) x P(B) = P(A and B), the events are independent.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26

  P(A) x P(B) = 0.26 Since P(A) x P(B) = P(A and B), the events are not independent.

• This cannot be determined since the number of males surveyed is not equal to the number of females surveyed.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26 and P(A or B) = 0.78 so the events are independent.

If event A and event B are independent, then which of the following is true?

• P(A) = P(B)

• P(A | B) = P(B)

• P(A | B) = P(A)

• P(A and B) = P(A) + P(B)

Suppose that the probabilities that an answer can be found on Google is 0.95, on Answers.com is 0.92, and on both websites is 0.874. Are the possibilities of finding the answer on the two websites independent?

• Yes, because (0.95)(0.92) = 0.874

• No, because (0.95)(0.92) = 0.874

• Yes, because 0.95 > 0.92 > 0.874

• No, because 0.5(0.95 + 0.92) ≠ 0.874

• There is insufficient information to answer this question.

• 1
• 2
• 3
• 4