What is Statistic: Definition and 122 Discussions

A statistic (singular) or sample statistic is any quantity computed from values in a sample that is used for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (aka mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose.
When a statistic is used to estimate a population parameter, the statistic is called an estimator. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the mean of a sample is an unbiased estimator of the population mean. This means that the expected value of the sample mean equals the true mean of the population.In descriptive statistics, a descriptive statistic is used to describe the sample data in some useful way. In statistical hypothesis testing, a test statistic is used to test a hypothesis. Note that a single statistic can be used for multiple purposes – for example the sample mean can be used to estimate the population mean, to describe a sample data set, or to test a hypothesis.

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  1. Govind

    I What is the correct definition of measurement uncertainty?

    I have some confusion regarding Measurement Uncertainity. In some books/articles it is defined wrt true value as "Uncertainty in the average of measurements is the range in which true value is most likely to fall , when there is no bias or systematic component of error is involved in...
  2. A

    I Probability to get a certain number or less by throwing two 6-faced die

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  3. red65

    B Concerning the birthday problem in probability

    The problem is stated like this : There are k people in a room. Assume each person’s birthday is equally likely to be any of the 365 days of the year (we exclude February 29), and that people’s birthdays are independent (we assume there are no twins in the room). What is the probability that two...
  4. I

    A Finding Minimal Mean Distance Curves on the Unit Sphere

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  5. red65

    B Where is the error in my reasoning about palindromes?

    Hello everyone, I found this problem online about probability, for me, I think that to have a 2 letter palindrome is less likely because we need to have the same letter in the 2 places which gives us 26 possibilities (aa , bb, cc ....) however for words with 3 letters we have 26 possibilities...
  6. red65

    B About the naive definition of probability

    hello, I took an introductory course about statistics, we viewed the naive definition of probability which says "it requires equally likely outcomes and can't handle an infinite sample space ", I understood that it requires finite sample space but I didn't understand "equally likely outcomes "...
  7. S

    Probability of Hypokalemia w/ 1 or Multiple Measurements

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  8. Mayhem

    I Shapiro-Wilks test and the order statistic

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  9. benagastov

    Finding all possible energy states faster without using a calculator

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  10. Y

    MHB Why are my p-value and test statistic values wrong?

  11. F

    A Calculating the variance of integrated Poisson noise on a defined quantity

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  12. S

    MHB What is a statistic and how is it used in various settings?

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  13. F

    A Computing a variance in astrophysics context

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  14. B

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  15. Amy_93

    I Statistic uncertainties in cross section plots - how to calculate?

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  16. gind_id

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  17. TheBigDig

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  18. U

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  19. Conservation

    I Nonparametric Hypothesis Tests

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  20. P

    Is Size 6 the Right Fit for Me? Understanding Mean, Median, and Mode

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  21. A

    I Statistics proof: y = k x holds for a data set

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  22. C

    Two teams, A and B, are playing a series of games

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  23. A

    I Discrete to continuum Gaussian function

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  24. A

    I Uncertainty of MonteCarlo Simulations: Weight and Error Bars

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  25. D

    A Estimation error from estimation quantile of normal distribution

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  26. Jarvis323

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  27. W

    A Defining a Symmetry Statistic to test for Normality?

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  28. Jakub

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  29. R

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  30. E

    I R-squared statistic for goodness-of-fit

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  31. R

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  32. L

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  33. D

    I How does the distribution depend on a variable resolution

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  34. G

    Minimize the sum of Type I and Type II errors

    Homework Statement Given X_1,\dots,X_n a simple random sample with normal variables (\mu, \sigma^2). We assume \mu is known but \sigma^2 is unknown. The hypothesis is \begin{cases} H_0: & \mu=\mu_0 \\ H_1: & \mu=\mu_1 > \mu_0 \end{cases} Determine the rejection region R...
  35. R

    Confusion between z and t values

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  36. R

    Help on determining independent events

    Homework Statement Hi, I have this question that I've been pondering for a while, I keep flipflopping on what I think is right. I only need help on the last part on whether the events are independent or not, the rest of the text is backstory to the question. I know for events to be independent...
  37. D

    Probability theory and statistics for Robotics and ME

    I study control theory and robotics. Recently I figured out that I have a much deeper understanding of probability and statistics compared to my colleagues. Is this 'talent' valuable in my field and if so, where? We used this theory to define white noise, but nothing more...as of now. Also I am...
  38. R

    Chi-square goodness of fit cannot find expected values

    Homework Statement An article in Business Week reports profits and losses of firms by industry. A random sample of 100 firms is selected, and for each firm in the sample, we record whether the company made money or lost money, and whether or not the firm is a service company. The data are...
  39. S

    I Calculating Probability with Poisson Distribution: Radioactive Source Counts

    Hello! I came across this problem: A counter near a long-lived radioactive source measures an average of 100 counts per minute. What is the probability that more than 110 counts will be recorded in a given one-minute interval? I am not sure how to do it. Applying the Poisson distribution formula...
  40. T

    I What is Yates' correction of contingency?

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  41. T

    I Level of significance and acceptance and rejection of the null hypothesis

    Why do we reject the null hypothesis in Goodness of fit when the Chi square statistic is less than the tabulated value of chi-square at say 5% level of significance and accept when it is more? What does it mean to have a Chi-square value more or less than the value assigned to a certain level...
  42. T

    I Understanding the null hypothesis

    I was reading Bio-statistics principles and practice by Antonisamy and stumbled upon the following: Null hypothesis is a hypothesis that suggests an absence of difference, association or effect, the negation of which provides evidence for presence of difference, association or effect. The only...
  43. T

    Maximum likelihood of a statistical model

    Homework Statement I look at the distribution ##(Y_1,Y_2,...,Y_n)## where ##Y_i=μ+(1+φ x_i)+ε_i## where ##-1<φ<1## and ##-1<x_i<1## . x's are known numbers. ε's are independent and normally distributed with mean 0 and variance 1. I need to find the the maximum likelihood estimator for μ and...
  44. N

    Calculating Energy Levels in a Ni2+ Ion Crystal

    Hello, I am stuck at the beginning of an exercise because I have some trouble to understand how are the energy level in this problem : In a crystal we have Ni2+ ions that we consider independent and they are submitted to an axial symmetry potential. Each ion acts as a free spin S=1. We have the...
  45. V

    A What is first and Second order Dependence?

    Can someone please explain to me what it means what they say a model is "first and second order dependence?"
  46. iikii

    Busy Barber Problem: Proportion of Time Apprentice is Busy

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  47. iikii

    Long-run proportion in state ′A′

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  48. Fasso

    I Probability of Particle Collision on a Closed Surface

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  49. HaLAA

    Roll a fair die 5 times

    Homework Statement Roll a fair die 5 times, find the probability that the first two rolls have the same outcomes. Homework EquationsThe Attempt at a Solution The total outcomes is 6^5, I think we have 6^2 * 6 choose 2 /6^5 since the first two numbers are fixed and we can choose 2 numbers from...
  50. A

    I Proof to the Expression of Poisson Distribution

    Hello. Given a range of time in which an event can occur an indefinite number of times, we say a random variable X folows a poisson distribution when it follows this statements: X is the number of times an event occurs in an interval and X can take values 0, 1, 2, … The occurrence of one event...
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