"If X^2=0 for a dataset, are the frequencies of the values in the contingency table all the same? Could I say that if the X^2 value of a dataset is 0, then the frequencies of the values of the cells in the contingency table are all the same? I have noticed that if I change the frequency of any of these values to be more than the other, that X^2 stops being 0. X^2=0"
Jannek93
Answered question
2022-10-06
Could I say that if the value of a dataset is 0, then the frequencies of the values of the cells in the contingency table are all the same? I have noticed that if I change the frequency of any of these values to be more than the other, that stops being 0.
Answer & Explanation
Peutiedw
Beginner2022-10-07Added 9 answers
The numbers in the rightmost column to the right of the vertical line are the sums of the numbers in the rows to the left of the line; the numbers in the bottom row below the horizontal line are the sums of the numbers in the columns above the line; the 35 in the lower right is the sum of the two numbers above it, or equivalently, of the two numbers to its left, or, again equivalently, of the four numbers in the table above and to the left of the margins.
Take the number in each cell in the table to be the number of individuals in the sample that fall in that cell. The null hypothesis says the probability that an individual is in a particular row is independent of which column that individual is in and vice-versa. The observed numbers are totals in the sample rather than in the population, so you generally won't see perfect independence in the sample even if the null hypothesis is true. Since they're based on the sample rather than on the whole population, if we say the probability of being in the first row is (taking the numbers 14 and 21 from the right margin), that is an estimate. Similarly we can estimate the probability of being in the first column as . The probability of being in the cell that is the upper left corner of the table, assuming that the null hypothesis of independence is true, is therefore estimated as Since the sample size is 35, the expected count in the first cell is therefore (and the obvious cancelation of 35 with 35 would happen even if all of the numbers had been different). Call this estimated expected value the expected count in the first cell.
In various chi-square tests (not all chi-square tests, but most chi-square tests that involve categorical data), the test statistic can be written as
If you work out the chi-square test statistic for the table with the particular numbers I've put there, you'll find it's exactly 0, simply because I chose the numbers to make that happen.
But the four numbers are not equal.
On the other hand, if you're doing the simple chi-square test of the null hypothesis that says an ordinary six-sided die is "fair", then the "expected" counts will each be 1/6 of the sample size---thus all equal to each other---and the chi-square test statistic then won't be 0 unless all six counts in the sample are equal.
Bottom line answer to your question: No.
New Questions in High school probability
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes?
Write formula for the sequence of -4, 0, 8, 20, 36, 56, 80, where the order of f(x) is 0, 1, 2, 3, 4, 5, 6 respectively
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.n=20,
p=0.7,
x=19
P(19)=
In binomial probability distribution, the dependents of standard deviations must includes.
a) all of above.
b) probability of q.
c) probability of p.
d) trials.The probability that a man will be alive in 25 years is 3/5, and the probability that his wifewill be alive in 25 years is 2/3
Determine the probability that both will be aliveHow many different ways can you make change for a quarter??
(Different arrangements of the same coins are not counted separately.)One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first passenger to board has misplaced his boarding pass and is assigned a seat at random. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?
A) 1
B) 0.33
C) 0.6
D) 0.5The value of is _______.
A)9
B)
C)
D)01 octopus has 8 legs. How many legs does 3 octopuses have?
A) 16
B 24
C) 32
D) 14From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...
A pack of cards contains aces, kings, queens and jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A B C D
You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner. (i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]
If A and B are two independent events such that , then the value of is
A)
B)
C)
D)The unit of plane angle is radian, hence its dimensions are
A)
B)
C)
D)Clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 340 babies were born, and 289 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born?
