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Can Z values be thought of as the number of standard deviations?

Yes. A Z value of a particular data point tells you how many standard deviations it is from its mean. Z=0 means it has the same value as the population mean, Z=-1 means it is 1std lower than its mean ...

Three questions about the article "Ditch p-values. Use Bootstrap confidence intervals instead"

"Am I right that this is not a p-value (which is the probability to see this or more extreme value of a test statistic)?" Good question! Yes, you're right, it's not a p-value. What's more ...
• 11.3k
Accepted

Why don’t we calculate the average of an entire given population instead of computing confidence interval to estimate the population mean?

We’d love to calculate population parameters! All of inferential statistics is about inferring. In other words, we are using our data at hand to guess about something greater than the data (e.g., the ...
• 32.4k
Accepted

Not getting 95% coverage for 95% t-distribution CI

Per @whuber's comment, np.std() provides a biased estimate of the sample standard deviation. Fortunately, the function allows you to correct for that by specifying ...
• 2,047
Accepted

Is it appropriate to put "error bars" on data when you have the full population?

Error bars show intervals; these intervals must represent something Error bars in a plot show an interval for a particular quantity, and like any element of a plot, these intervals must actually ...
• 97.2k

Confidence intervals around functions of estimated parameters

Usually we take normality assumption for linear regression models. That is, $y_i\sim N(\beta^Tx_i,\sigma^2)$. From this assumption we derive the asymptotic distribution of $\hat{\beta}$, which is also ...
• 2,381
Accepted

Three questions about the article "Ditch p-values. Use Bootstrap confidence intervals instead"

1 They don’t mean what people think they mean Am I right that this is not a p-value (which is the probability to see this or more extreme value of a test statistic)? Is it a correct procedure for a ...
• 48.4k

• 3,111
Accepted

How can we know population mean but not variance

$\mathbf{\mu}$ is the theorized value under the null hypothesis. For the situation in general: $$H_0:\mu = \mu_0\\ H_a:\mu\ne\mu_0$$ We do our usual fun of calculating the sample mean $\bar x$ and ...
• 32.4k

Difference between statements about confidence intervals

The sample proportion is different to the population proportion. The first one is a known quantity that you can compute from your sample, whereas the second one is the unknown quantity that you are ...
• 97.2k
Accepted

Chi-squared confidence interval for variance

Because the chi-squared distribution is skewed, the sample variance is not generally at the center of a 95% CI for the variance (for normal data). You are correct to say that you can often get a ...
• 50.8k

Chi-squared confidence interval for variance

For univariate continuous asymmetric distributions the highest density region (HDR) can be found by solving a constrained optimisation problem for the boundary points. You are correct that this ...
• 97.2k
Accepted

Post-hoc power analysis for null results: how to use 95% confidence interval instead?

If your CIs are narrow, then you have an idea of how large the effect is, and you can say with some confidence that the effect is small, and that's why you didn't detect it. If the CIs are wide, then ...
• 14.8k