In statistics many a times note is added as "correlation is significant at the 0.05 and 0.01 levels"
In simplified means what does it mean?
Is it same as the confidence interval that can be set in excel correlation analysis module.
If confidence interval is not set in excel, say 95%, then at what significance the correlation coefficients are given by excel.
@Chalamalla,
it is important to stress the difference between the common and the statistical meaning of the word "significance". However, your explanation of statistical significance is wrong and misleading.
Correct is: statistical significance ("p-value") is the probability of a more extreme test statistic than the one calculated from the observed data, under a given model.
It tells you something about the data and not about a "truth". At no time there is a concept of "truth" involved in the whole testing procedure. We have a model, and the test tells us - to phrase it in a bit more simple way - how well the data can be explained by this model. A low p-value (high statistical significance) means that the model is clearly unable to describe all features of the data well. Given the context of the model and the source/generation and kind of the data, this finding may be an indication that the model is unsuited to describe the data.
When the model is a restricted version of larger model that must be able to describe all features of the data, then we can attribute the unsuitedness to this restriction. This restriction is usually called the "null hypothesis", the hypothesis that is "tested". A low p-value is then interpretable as an indication that the restriction (the "null hypothesis") makes the model unsuited to explain the data, and that therefore this hypothesis should be rejected and that the full (unrestricted) model should better be used to explain the data.
The decision on which model to use (the restricted or the unrestricted) is not only based on the p-value but also on the entire context of the research (plausibility of the model, experimental design, particular difficulties, sample sizes, estimated effect sizes, related subject knowledge etc). Rejecting the null hypothesis just(!) because p
Sachin. It is just like speaking, one is 95% or 99% confident of the result. Best,
The sentence is obvioulsly related to "null-hypothesis significance testing" (NHST), what is a logically flawed procedure, so there is no logically correct explanation about the meaning one could give. Further, the sentence is phrased wrongly, as it is not the correlation that can be significant but the observed data under the model and the tested hypothesis.
In short, the sentence tells us that they found "p < 0.01" for some test on the correlation, but there is no information what hypothesis is tested in what model. This information alone is absolutely meaningless in any further way, there is no further explanation or conclusion that could be derived from this fact.
The p-value is related to the (1-p)-confidence interval. The (1-p)-confidence interval just ends at the value of the tested hypothesis. When the p-value obtained for the hypothesis r=0 was 0.02, then on limit of the 98%-confidence interval of the estimated r would just be at r=0, all confidence intervals with lower confidence levels would not include r=0, and all intervals with higher confidence levels would include r=0.
Saying that p99%, so the 99% interval will (just) not include the tested value. Since the 95% inteval is smaller, it won't include the tested value either.
It simply means that while testing the hypothesis that population has a specified correlation correlation coefficient on the basis of sample information we draw conclusion about population correlation coefficient.
Thank you all
I wanted simple answer, and I think I got it.
@Naik sir thank u again.
At 0.05 level we simply interpret that out of 100 samples 95 times we get the correct information about population on the basis of sample and similarly for 0.01
@Chalamalla,
it is important to stress the difference between the common and the statistical meaning of the word "significance". However, your explanation of statistical significance is wrong and misleading.
Correct is: statistical significance ("p-value") is the probability of a more extreme test statistic than the one calculated from the observed data, under a given model.
It tells you something about the data and not about a "truth". At no time there is a concept of "truth" involved in the whole testing procedure. We have a model, and the test tells us - to phrase it in a bit more simple way - how well the data can be explained by this model. A low p-value (high statistical significance) means that the model is clearly unable to describe all features of the data well. Given the context of the model and the source/generation and kind of the data, this finding may be an indication that the model is unsuited to describe the data.
When the model is a restricted version of larger model that must be able to describe all features of the data, then we can attribute the unsuitedness to this restriction. This restriction is usually called the "null hypothesis", the hypothesis that is "tested". A low p-value is then interpretable as an indication that the restriction (the "null hypothesis") makes the model unsuited to explain the data, and that therefore this hypothesis should be rejected and that the full (unrestricted) model should better be used to explain the data.
The decision on which model to use (the restricted or the unrestricted) is not only based on the p-value but also on the entire context of the research (plausibility of the model, experimental design, particular difficulties, sample sizes, estimated effect sizes, related subject knowledge etc). Rejecting the null hypothesis just(!) because p
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