As N increases, how does the size of SEM change (assuming the s stays the same)?
SEm = SD/√n
What does that tell you?
To understand how the size of the Standard Error of the Mean (SEM) changes as N (sample size) increases, it is important to grasp the concept of SEM and its calculation.
The SEM measures the variability or spread of the sample mean around the population mean. It quantifies the average amount that the sample mean is expected to deviate from the true population mean. The formula to calculate SEM is:
SEM = s / √N
where s is the standard deviation of the sample and N is the sample size.
Now, let's analyze how the size of SEM changes as N increases, assuming s (standard deviation) remains the same:
1. As N increases: As the sample size (N) grows larger, the denominator (√N) of the SEM formula increases. This expansion of the denominator contributes to the reduction of SEM size. In simpler terms, as the dataset expands, the effect of the square root of N decreases.
2. Assuming s stays the same: When the standard deviation (s) remains constant, the numerator of the SEM formula does not change. Since only the denominator (√N) increases due to the larger sample size, the SEM decreases proportionally. This means that as N increases, the spread or variability of the sample means around the population mean diminishes.
In summary, as the sample size (N) increases while the standard deviation (s) remains constant, the size of SEM decreases. A larger sample size generates more precise estimates, resulting in smaller variability and a more accurate representation of the population mean.