Question

With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant?

Answer 1

With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant.

Step-by-step explanation:

With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant. This is because as the sample size increases, the variability decreases, making it easier to detect even small deviations from the null value. Statistical significance is determined by calculating the p-value, which measures the probability of obtaining the observed data or more extreme values under the null hypothesis. If the p-value is below a predetermined threshold (often 0.05 or 0.01), the effect size is considered statistically significant.

For example, let's say we are comparing the mean scores of two groups using a t-test. If we have a large sample size, any small differences in the means between the groups will have a lower p-value, indicating statistical significance. This means that the observed difference is unlikely to have occurred by chance and can be attributed to a real difference between the groups.