Statistics question: I'm having trouble understanding my statistics professor's objection to this interpretation of confidence intervals.(adsbygoogle = window.adsbygoogle || []).push({});

If you have some distribution with parameter x: X = Dist(x), and you perform a random experiment drawing N random variables from it, and derive from those some estimator y related to x, then I *want* to say the following, but my statistics prof insists it's an invalid interpretation:

If you have a space with the (unknown) parameter x and the statistic y, for each x there is a conditional probability distribution for the y that will be yielded from a draw of N variables. This leads to a joint probability distribution linking x and y. Now that you have a value for y, you are in a subspace of the space (y=whatever you got), and there is a distribution of probability for x. The probability that you find x within a certain range relates to this distribution.

My statistics prof objects that x is a specific value, not a random variable. While I understand that x *in fact* is either within or not within the interval, the best you can give with the imperfect information available is a finite probability. You have limited knowledge due to the statistic y, which is more than no knowledge and less than exact knowledge of what the parameter x is.

He insists you cannot make a probability statement about it, and that known confidence intervals don't give you any information about the underlying distribution, only future ones. That x either is or is not within any distribution, and that you cannot say anything about it.

(I already understand the point about a certain proportion of future confidence interval draws containing the parameter).

I don't know why you can't do this. Can anyone try to enlighten me? Any perspectives you have might help me understand the error.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Interpretation of Confidence Intervals and the like

Loading...

Similar Threads - Interpretation Confidence Intervals | Date |
---|---|

A Interpreting a paper on spectral analysis | Mar 14, 2018 |

A Interpreting Chi Squared ... backward | Feb 11, 2018 |

I Interpreting the correlation | Feb 6, 2018 |

I Bayes again - how to interpret in vitro genotoxicity data | Jun 10, 2017 |

Confidence interval interpretation mistake | Jul 4, 2013 |

**Physics Forums - The Fusion of Science and Community**