JP Monteagudo

::: {#rq-what-exactly-is-the-clt-and-whats-the-deal-with-n-geqslant-30 .section .level2}
## RQ: What exactly is the CLT and what's the deal with n ![](https://latex.codecogs.com/png.latex?%20%5Cgeqslant%20) 30? {#rq-what-exactly-is-the-clt-and-whats-the-deal-with-n-30 .anchored anchor-id="rq-what-exactly-is-the-clt-and-whats-the-deal-with-n-geqslant-30"}

- CLT - mathematical definition and simple terms definition

- How we use CLT

- How to know when empirical distribution converges to normal
  distribution?

- How did we come up with n \$ \$ 30?

  - Cohen (1991) Taught that at least 30 observations were needed to use
    critical-ratio approach used in t-tables when comparing groups. If
    sample size smaller than 30, then students would be forced to
    "small" sample statistics.

    > It wasn't until some years later that I discovered (mind you, not
    > invented) power analysis, one of whose fruits was the revelation
    > that for a two-independent-group-mean comparison with n = 30 per
    > group at the sanctified two-tailed .05 level, the probability that
    > a medium-sized effect would be labeled as significant by the most
    > modern methods (a t-test) was only .47. Thus, it was approximately
    > a coin flip whether one would get a significant result, even
    > though, in reality, the effect size was meaningful.

    - Simply a rule of thumb that allowed students to use critical
      t--tables. These tables could only span 30 lines to fit in one
      page. Fisher created the t--table and only went up to n = 30
      (Fisher's *Statistical Methods for Research Workers* (1925))
    - Sample size at least 30 so that the error variance between
      t--t-distribution and theoretical normal distribution is .25 or
      less from df = 30 up to infinity.
    - When data is severely skewed neither the t--test nor the
      permutation test have much power (are not robust) to correctly
      identify a statistically significance difference in means between
      too highly skewed distributions. Even if your data contained tens
      of thousands of observations, the t--test may not recognize a
      statistically significance difference in means. The distribution
      of the data and the number of observations need to be considered
      when deciding whether the t--test is meaningful and accurate,
      sometimes thousands of observations may be needed.

  ## Solution {#solution .anchored}

  - Use power analysis to determine the sample size needed to obtain
    statistically significant results using your desired
    ![](https://latex.codecogs.com/png.latex?%5Calpha),
    ![](https://latex.codecogs.com/png.latex?%5Cbeta) and effect size
    measure. This way, you don't have to assume
:::

::: {#quarto-appendix .default}
::: {#quarto-citation .section .quarto-appendix-contents}
## Citation {#citation .anchored .quarto-appendix-heading}

<div>

::: {.quarto-appendix-secondary-label}
BibTeX citation:
:::

``` {.sourceCode .code-with-copy .quarto-appendix-bibtex}
@online{monteagudo2024,
  author = {Monteagudo, JP},
  title = {“{\{Can} {I} Have the {CLT,} Please– a Straightforward
    Explanation of the {Central} {Limit} {Theorem} and the Magic
    \textbackslash(n \textbackslash Geqslant 30\textbackslash)\}”},
  date = {2024-03-06},
  url = {https://www.jpmonteagudo.com/blog/2024/02/clt},
  langid = {en}
}
```

::: {.quarto-appendix-secondary-label}
For attribution, please cite this work as:
:::

::: {#ref-monteagudo2024 .csl-entry .quarto-appendix-citeas}
Monteagudo, JP. 2024. "'{Can I Have the CLT, Please-- a Straightforward
Explanation of the Central Limit Theorem and the Magic \\n \Geqslant
30\\}'." March 6, 2024. <https://www.jpmonteagudo.com/blog/2024/02/clt>.
:::

</div>
:::
:::


RQ: What exactly is the CLT and what’s the deal with n  30?   CLT - mathematical definition and simple terms definition  How we use CLT  How to know when empirical distribution converges to normal distribution? How did we come up with n $ $ 30?  Cohen (1991) Taught that at least 30 observations were needed to use critical-ratio approach used in t-tables when comparing groups.

Rogue Scholar Posts

“{Can I have the CLT, please– a straightforward explanation of the Central Limit Theorem and the magic (n )}”