Suppose you and a friend each take different random samples of data pairs (x,y) from the same population. Assume the samples are the same size. Based on your samples, you compute r = 0.83. Based on her sample your friend computes 0.79. Is your friend’s value for r wrong? Explain
No. Different samples, from the same population may result in different value for sample statistic r.
Suppose you and a friend each take different random samples of data pairs (x,y) from the same population. Assume the samples are the same size. Based on your samples, you compute r=0.83. Based on her sample, your firmed computes r=0.79
Is your friends value wrong? Explain?
No, your friend's value for r is not necessarily wrong. The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between two variables. In this case, you and your friend computed the correlation coefficient separately based on different random samples from the same population.
Since you and your friend took different random samples, it is expected that you might get slightly different correlation coefficients. These differences can be due to the random nature of sampling, as well as the variability in the data within the population.
In this scenario, your computed value of r = 0.83 and your friend's computed value of r = 0.79 are relatively close to each other. Both values indicate a strong positive linear relationship between the variables you and your friend used in your analysis. As long as the computations are done correctly, there is no reason to dismiss your friend's value as wrong.
However, it is important to note that correlation coefficients are estimates based on sample data and are subject to sampling variability. To get a more accurate estimate of the true correlation in the population, you would need a larger sample size or attempt multiple samples.
To determine if your friend's value for r is wrong, we need to consider the nature of correlation coefficient (r) and its interpretation.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables (x and y) in a given sample of data. It ranges from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship between the variables.
In this case, you and your friend took different random samples of data pairs (x,y) from the same population. It is important to note that the correlation coefficient (r) can vary slightly between samples due to random chance, even when sampling from the same population.
Since both you and your friend obtained correlation coefficients close to each other (0.83 and 0.79), it suggests that there is a relatively strong positive linear relationship between the variables in both samples. The slight difference in the values of r could be attributed to random sampling variability.
Therefore, it would not be accurate to say that your friend's value for r is wrong. It simply indicates a slightly different estimate of the correlation coefficient based on her specific sample. If you both had computed significantly different values of r, it might be worth examining the data or the methodology used to calculate the correlation coefficient to ensure accuracy.
It is also important to note that the correlation coefficient alone does not provide a complete picture of the relationship between variables. Other factors such as sample size, outliers, and the presence of non-linear relationships should also be considered when interpreting the results.