One disadvantage of using a large sample size is that it can lead to the detection of statistically significant differences that are not practically significant, potentially resulting in misleading conclusions. Additionally, larger samples can be more costly and time-consuming to collect and analyze, requiring more resources. There is also a risk of overfitting in complex models, where the model captures noise rather than the underlying trend.
"The advantage is that the mean takes every value into account. A disadvantage is that it can be affected by extreme values. " The mean or more properly the "arithmetic mean" of a sample will eventually approximate the mean of the distribution of the population as the sample size increases. If the population distribution is skewed (not symmetrical), the mode and median will not provide an estimate of the mean, even as the sample size becomes large.
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
no
that you have a large variance in the population and/or your sample size is too small
Better the results
A disadvantage to a large sample size can skew the numbers. It is better to have sample sizes that are appropriate based on the data.
Statistically the larger the sample size the more significant the results of the experiment are. Chance variation is ruled out.
"The advantage is that the mean takes every value into account. A disadvantage is that it can be affected by extreme values. " The mean or more properly the "arithmetic mean" of a sample will eventually approximate the mean of the distribution of the population as the sample size increases. If the population distribution is skewed (not symmetrical), the mode and median will not provide an estimate of the mean, even as the sample size becomes large.
Yes, but that begs the question: how large should the sample size be?
A sample size of one is sufficient to enable you to calculate a statistic.The sample size required for a "good" statistical estimate will depend on the variability of the characteristic being studied as well as the accuracy required in the result. A rare characteristic will require a large sample. A high degree of accuracy will also require a large sample.
The result will be closer to the truth.
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
no
that you have a large variance in the population and/or your sample size is too small
Better the results
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
A small sample size and a large sample variance.