Hi, I want to know, how I will convert p value into t statistics (t score or t distribution score) appropriately?
Then how i will convert that t statistics into z statistics or score? Please suggest accurate way or formula. ]
Thank you
You can find the CDF (cumulative distribution function) in the Wikipedia article about the t-distribution. Plug in the degrees of freedom and the t-quantile (tobs) to get the corresponding probebility value for Pr(t < tobs).
There is no way to convert a t into a z statistic. These are different measures. There is only an approximate equality between t and z when the fegrees of freedom are large (infinitive). The "exact" formula is then (->inifinite degrees of freedom): z=t.
https://en.wikipedia.org/wiki/Student's_t-distribution
To find the t score is nothing just only value of t such that P[T>t]=p, where T is having student t distribution. You may use the command qt(pvalue, df, lower=FALSE) in R Software.
z-scores and t-scores both are a conversion of individual scores into a standard form. However, t-scores are used when the conversion is made without knowledge of the population standard deviation and mean. Seeing as you don’t know those parameters for your population, you make an estimate by using the statistics from your sample.
If you want to calculate a t-statistic for a corresponding p-value, you just need to know if the p-value is one-sided or two-sided and the degrees of freedom for the t-distribution. Then you can simply use the quantile function of the t-distribution to get a t-value (see the R-code of Arun's answer).
From df = 30 onwards the t-distribution can be approximated by the standard normal distribution. This fact might answer part two of the question.
It depends on your hypotheses:
1) Bilateral: H0: mu = mu0 versus H1: mu != mu0, then, (using R commands),
T can be either qt (Pvalue / 2, df) or -qt (Pvalue / 2, df)
2) Left sided: If H0: mu> = mu0 versus H1: mu < mu0, then,
T = qt (Pvalue, df)
3) Right sided: H0: mu mu0, then,
T = -qt (1 - Pvalue, df)
Similar to the answers above, and not exactly what you asked, but I found this helpful: This goes p-val to t-val to standardized mean difference.
http://www.metafor-project.org/doku.php/tips:assembling_data_smd
adding to the thread in case it can help someone else.
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