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### Why do I need to rounding x and y values to the nearest 0.5 when manually calculating correlation?

I'm trying to calculate correlation using a formula in Statistics 4th Edition by Freedman: r = average of (x in standard units) * (y in standard units) If I try this out ... ...
146 views

### A/B test and SRS

I was reading about Simple Random Sampling (SRS) from this lecture notes. It says that SRS, which actually is a sampling without replacement makes $x_i$ not independent. Then I thought about A/B ...
111 views

### Statistical analysis for replication in very small experimental datasets

A colleague does replication on a quite coslty experiments. There are four different conditions, each one duplicated. The outcome with $4\times 2 = 8$ points is illustrated below: The analysis is ...
141 views

### What is the expected value of sample variance in this problem?

Let $x_1,x_2,..x_{21}$ be a random sample from a distribution having variance 5. Let $$\bar X = \frac1{21}\sum_{i=1}^{21}X_i\quad\text{and}\quad S=\frac1{21}\sum_{i=1}^{21}(X_i-\bar X)^2$$ What is ...
136 views

### Which are the expressions for the variance and standard deviation of a sample?

I have checked several offline and online resources, and they are conflictive. Some define the sample variance as $$s_n^2 = \frac{\sum_{i}^{n}(x_i-\overline{x})^2}{n}$$ That is just the second ...
123 views

### What are biased and inefficient estimators?

I’m studying statistics from Schaum’s Outline, which gives the following: ...
40 views

### “… because sample mean gets different values from sample to sample and it is a random variable with mean $\mu$ and variance $\frac{\sigma^2}{n}$.”

This answer by user "sevenkul" says the following: The sample mean $\overline{X}$ also deviates from $\mu$ with variance $\frac{\sigma^2}{n}$ because sample mean gets different values from ...