What is the hair 10 times rule?

Author: Harmon Wilkinson  |  Last update: Saturday, May 31, 2025

The ten-times rule is widely used in PLS-SEM and suggests that the sample size should be at least 10 times the maximum number of arrows pointing at a construct in the model (Hair et al., 2022), which, for the present analysis would be 6 arrows (see Fig. 1). ...

What is the 10 times rule in Hair et al 2011?

A widely used minimum sample size estimation method in PLS-SEM is the “10-times rule” method (Hair et al., 2011), which builds on the assumption that the sample size should be greater than 10 times the maximum number of inner or outer model links pointing at any latent variable in the model.

What is the 10 percent rule for sample size?

10 Percent Rule: The 10 percent rule is used to approximate the independence of trials where sampling is taken without replacement. If the sample size is less than 10% of the population size, then the trials can be treated as if they are independent, even if they are not.

What is the empirical validation of the 10 times rule for SEM?

The prominent 10-times rule suggests that the minimum sample size should be 10 times the maximum number of arrowheads pointing at a latent variable anywhere in the partial least squares path model. Despite its prominence in research practice, this rule of thumb lacks systematic validation.

What is the minimum sample size for Smartpls?

Re: 10 times rule

Yes, based on that rule of thumb your minimum sample size is 30. However, that does not mean that such a sample size is sufficient for detecting small effects or for estimating robust parameters from which you can draw generalizable conclusions.

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What is the 10 times rule for sample size?

The ten-times rule is widely used in PLS-SEM and suggests that the sample size should be at least 10 times the maximum number of arrows pointing at a construct in the model (Hair et al., 2022), which, for the present analysis would be 6 arrows (see Fig.

Why is 30 the minimum sample size?

Why is 30 the minimum sample size? The rule of thumb is based on the idea that 30 data points should provide enough information to make a statistically sound conclusion about a population. This is known as the Law of Large Numbers, which states that the results become more accurate as the sample size increases.

What is the minimum sample size for SEM?

Despite this, various rules-of-thumb have been advanced, including (a) a minimum sample size of 100 or 200 (Boomsma, 1982, 1985), (b) 5 or 10 observations per estimated parameter (Bentler & Chou, 1987; see also Bollen, 1989), and (c) 10 cases per variable (Nunnally, 1967).

What is the rule of thumb for sample size?

Summary: The rule of thumb: Sample size should be such that there are at least 5 observations per estimated parameter in a factor analysis and other covariance structure analyses. The kernel of truth: This oversimplified guideline seems appropriate in the presence of multivariate normality.

Is 200 respondents enough for a survey?

As a very rough rule of thumb, 200 responses will provide fairly good survey accuracy under most assumptions and parameters of a survey project. 100 responses are probably needed even for marginally acceptable accuracy.

What is the 10 rule formula?

Step 1: Identify the population size, , and calculate 10% of the population size, . Step 2: Identify the sample size, . Step 3: Compare the sample size to 10% of the population size. If n ≤ 0.1 N then the 10% rule is satisfied.

Is 10 sample size statistically significant?

While there are many sample-size calculators and statistical guides available, those who never did statistics at university (or have forgotten it all) may find them intimidating or difficult to use. A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000.

What is the 2 inch Hair rule?

A brief summary of the 2.25-inch rule: Grab a ruler and a pencil. Place the pencil horizontally under your chin and the ruler vertically at your earlobe (see the image above). If the pencil and the ruler meet at a point less than 2.25 inches from your ear, chop away.

What is a good sample size for a study?

For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample. For larger populations, such as a population of 10,000, a comparatively small minimum ratio of 10 percent (1,000) of individuals is required to ensure representativeness of the sample.

What is the difference between PLS-SEM and SEM?

“The philosophical distinction between CB‑SEM and PLS‑SEM is straightforward. If the research objective is theory testing and confirmation, then the appropriate method is CB‑SEM. In contrast, if the research objective is prediction and theory development, then the appropriate method is PLS‑SEM.

What is the formula for calculating sample size?

Sample Size = N / (1 + N*e2)

Note that this is the least accurate formula and, as such, the least ideal. You should only use this if circumstances prevent you from determining an appropriate standard of deviation and/or confidence level (thereby preventing you from determining your z-score, as well).

What is the general rule in the sample size?

EXISTING RULES/GUIDELINES OF SAMPLE SIZE

The ratio should not be less than 5-to-1 (Gorsuch, 1983; Hatcher, 1994; Suhr, 2006). For example, a study with 30 items (questions) would require 150 respondents.

What is the slovin formula?

n = N / (1+Ne^2)

Where 'n' is your sample size. Let's say that you want a survey that represents approximately 10,000 people. You're alright with a margin of error of 6%. Using just this much information, we can undertake the sample size calculation using Slovin's Formula.

What is the rule of thumb for SEM?

A widely accepted rule of thumb is 10 cases/observations per indicator variable in setting a lower bound of an adequate sample size (Nunnally, 1967). Very often attention is given to the ratio of (N:q) of ... Get Structural Equation Modeling: Applications Using Mplus now with the O'Reilly learning platform.

Does SEM increase with sample size?

Standard error formula

From the formula, you'll see that the sample size is inversely proportional to the standard error. This means that the larger the sample, the smaller the standard error, because the sample statistic will be closer to approaching the population parameter.

What is the rule of thumb for CFA?

Common rules of thumb for determining adequate N for a particular application of CFA include, but are not limited to: N ≥ 200, ratio of N to the number of variables in a model (p), N/p ≥ 10; the ratio of N to the number of model parameters (q), N/q ≥5; and an inverse relationship between construct reliability and ...

What is the smallest acceptable sample size?

Some researchers do, however, support a rule of thumb when using the sample size. For example, in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30.

What is the Cochran's formula?

Cochran formula is the typical formula used, as it calculates for a certain precision within a large enough population. Where n is the sample size, z is the z-value associated with the confidence chosen, p is the standard deviation, q is (1-p), and e is the margin of error.

When to use t-test vs z-test?

Generally, z-tests are used when we have large sample sizes (n > 30), whereas t-tests are most helpful with a smaller sample size (n < 30). Both methods assume a normal distribution of the data, but the z-tests are most useful when the standard deviation is known.

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