Mark Rubin

In this paper ([Rubin,
20](https://www.google.com/url?q=https%3A%2F%2Fdoi.org%2F10.1007%2Fs11229-019-02433-0&sa=D&sntz=1&usg=AFQjCNEVuCuq3elOVD71HY_Ee1DN_5q1Og)21),
I consider two types of Type I error probability. The *Neyman-Pearson
Type I error rate* refers to the maximum frequency of incorrectly
rejecting a null hypothesis if a test was to be repeatedly reconducted
on a series of different random samples that are all drawn from the
exact same null population. Hence, the Neyman-Pearson Type I error rate
refers to a long run of *exact* replications. In contrast, the
*Fisherian Type I error probability* is the probability of incorrectly
rejecting a null hypothesis in relation to a hypothetical population
that reflects the relevant characteristics of the particular sample
under consideration. Hence, the Fisherian Type I error rate refers to a
one-off sample rather than a series of samples that are drawn during a
long run of exact replications.

I argue that social science deals with units of analysis (people, social
groups, and social systems) that change over time. As the Greek
philosopher Heraclitus put it: "No man ever steps in the same river
twice, for it's not the same river and he's not the same man." Rivers
and men are what Schmidt (2009, p. 92) called "irreversible units" in
that they are complex time-sensitive systems that accumulate history.
The scientific investigation of these irreversible units cannot proceed
on the assumption that exact replications are possible. Consequently,
the Neyman-Pearson Type I error rate is irrelevant in social science,
because it relies on a concept of exact replication that cannot take
place in the case of people, social groups, and social systems. Why
should social scientists be interested in an error rate for an
impossible process of resampling from the same fixed and unchanging
population?

<figure>
<img
src="https://cdn-images-1.medium.com/max/554/1*zfDlYm8FEwiXhSQ8QrnI2g.jpeg" />
<figcaption>Source: <a
href="https://images.app.goo.gl/RiEP5tPX75AVbmFy6">https://images.app.goo.gl/RiEP5tPX75AVbmFy6</a></figcaption>
</figure>

I argue that the Fisherian Type I error probability is more appropriate
in social science because it refers to one-off samples from hypothetical
populations. In this case, researchers recognise that every sample comes
from a potentially different population. Hence, researchers can apply
the Fisherian Type I error probability to each sample-specific
provisional decision that they make about rejecting the same substantive
null hypothesis in a series of *direct* replications.

I conclude that the replication crisis may be partly (not wholly) due to
researchers' unrealistic expectations about replicability based on their
consideration of the Neyman-Pearson Type I error rate across a long run
of exact replications.

For further information, please see:

Rubin, M. (2021). What type of Type I error? Contrasting the
Neyman-Pearson and Fisherian approaches in the context of exact and
direct replications. *Synthese, 198,* 5809--5834*. *.
[https://doi.org/10.1007/s11229-019-02433-0](https://www.google.com/url?q=https%3A%2F%2Fdoi.org%2F10.1007%2Fs11229-019-02433-0&sa=D&sntz=1&usg=AFQjCNEVuCuq3elOVD71HY_Ee1DN_5q1Og)
\*[Self-archived
version](https://drive.google.com/file/d/10mEkuIElCGE5lYO-24HCYS8NKfytZBpG/view?usp=sharing)\*

I also discuss the differences between the Fisherian and Neyman-Pearson
approaches to hypothesis
testing [here](https://sites.google.com/site/markrubinsocialpsychresearch/replication-crisis/repeated-sampling).

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In this paper (Rubin, 2021), I consider two types of Type I error probability. The
<em>
 Neyman-Pearson Type I error rate
</em>
refers to the maximum frequency of incorrectly rejecting a null hypothesis if a test was to be repeatedly reconducted on a series of different random samples that are all drawn from the exact same null population. Hence, the Neyman-Pearson Type I error rate refers to a long run of
<em>
 exact
</em>
replications.

Rogue Scholar Posts

What Type of Type I Error?