One may ask why sample size is so important. The answer to this is that an appropriate sample size is required for validity. If the sample size it too small, it will not yield valid results. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30.

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It’s not that “30 in a sample group should be enough” for a study. It’s that you need at least 30 before you can reasonably expect an analysis based upon the normal distribution (i.e. z test) to be valid. That is it represents a threshold above which the sample size is no longer considered “small”.

A higher confidence level requires a larger sample size. Power – This is the probability that we find statistically significant evidence of a difference between the groups, given that there is a difference in the population. A greater power requires a larger sample size.

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As a rough rule of thumb, many statisticians say that a sample size of 30 is large enough. If you know something about the shape of the sample distribution, you can refine that rule. The sample size is large enough if any of the following conditions apply. The population distribution is normal.

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First, chi-square is highly sensitive to sample size. As sample size increases, absolute differences become a smaller and smaller proportion of the expected value. Generally when the expected frequency in a cell of a table is less than 5, chi-square can lead to erroneous conclusions. …

The chi-square test is sensitive to sample size. The chi-square test cannot establish a causal relationship between two variables.

There are three different measures of effect size for chi-squared test, Phi (φ), Cramer’s V (V), and odds ratio (OR). V = χ 2 n · d f , where n is total number of observation, and df is degrees of freedom calculated by (r – 1) * (c – 1). Here, r and c are the numbers of rows and columns of the contingency table.

The effect size of the population can be known by dividing the two population mean differences by their standard deviation.

The phi coefficient ranges from −1 to +1, with negative numbers representing negative relationships, zero representing no relationship, and positive numbers representing positive relationships.

Effect size tells you how meaningful the relationship between variables or the difference between groups is. It indicates the practical significance of a research outcome. A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

An effect size is exactly equivalent to a ‘Z-score’ of a standard Normal distribution. For example, for an effect-size of 0.6, the value of 73% indicates that the average person in the experimental group would score higher than 73% of a control group that was initially equivalent.

The statistical power of a significance test depends on: • The sample size (n): when n increases, the power increases; • The significance level (α): when α increases, the power increases; • The effect size (explained below): when the effect size increases, the power increases.

Like statistical significance, statistical power depends upon effect size and sample size. If the effect size of the intervention is large, it is possible to detect such an effect in smaller sample numbers, whereas a smaller effect size would require larger sample sizes.

G*Power is a tool to compute statistical power analyses for many different t tests, F tests, χ2 tests, z tests and some exact tests. G*Power can also be used to compute effect sizes and to display graphically the results of power analyses.

Higher sample size allows the researcher to increase the significance level of the findings, since the confidence of the result are likely to increase with a higher sample size. This is to be expected because larger the sample size, the more accurately it is expected to mirror the behavior of the whole group.

The difference is sample size. The more data we have, the more precisely we can pin down where the population mean could be… so a fixed value of the mean that is wrong will look less plausible as our sample sizes become large. That is, p-values tend to become smaller as sample size increases, unless H0 is true.

Increasing the sample size will tend to result in a smaller P-value only if the null hypothesis is false, which is the point at issue. However, it is possible to justify using a larger alpha when the sample size is small by considering the probabilities of both type I and type II errors.