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What was the general approach to performing statistics before calculations were fully computerised (i.e. before both calculation and memory were managed by computer)?

I understand the question could become rather broad, so I'm mainly looking for illustrative impressions of the techniques, attitudes and approaches people employed to extract meaning out of data when all you had was a pen, paper and some other mechanical tools.


I suspect that something as simple (to modern statisticians) as linear regression with, say, 100 rows and three variables, would've been rather daunting to someone performing the matrix operations manually. But if an analysis was important, it would've been worth spending the day doing number crunching, or have a room full of human calculators do it for you. But this is still missing a lot of the pre-analysis work (stuff like visualisation, removal of extreme values, etc) that we take for granted today. How would a large regression have been approached back then? What were the shortcuts and clever labour-saving tricks?

I also suspect that many tests (t test, F test, other tests that involve taking a sample of the data) were used much more regularly back then to get a handle on the general feel of the data. Would this be correct?

Finally, were analyses by and large restricted to problems for which analytical solutions could be found?

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    $\begingroup$ What does "computational data processing" mean precisely? Mechanical calculators have a long history. I remember teaching their use in the early 1970s. Iterative methods for fitting logit and probit methods were routine in the 1940s and 1950s, although naturally enormously more work than now. $\endgroup$ – Nick Cox Jul 28 '18 at 10:32
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    $\begingroup$ So, you mean "electronic computers" from say the middle 1940s on. (Computers were, seriously, the people who did the computing for some decades, usually women.) $\endgroup$ – Nick Cox Jul 28 '18 at 11:00
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    $\begingroup$ Look at textbooks of the time to see what was routine. e.g. Yule and Kendall, Snedecor. Nevertheless those can be misleading. For example, I once went through some classic texts on analysis of variance (Cochran and Cox, Scheffé, etc.) and could find no examples whatsoever of graphs based on data. Does that mean that generation didn't know about plotting data? I don't think so. It's just as likely that plotting data was regarded as too obvious to deserve mention. Also, generations accustomed to hand or mechanical calculation trained themselves and students to watch out for possible outliers. $\endgroup$ – Nick Cox Jul 28 '18 at 11:21
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    $\begingroup$ You might find this interesting. $\endgroup$ – Scortchi - Reinstate Monica Jul 28 '18 at 12:39
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    $\begingroup$ Many historians trace the origin of modern statistics to an exchange of letters between Blaise Pascal and Pierre de Fermat in 1654. Somewhat coincidentally, Pascal had invented (and built) a mechanical calculator 12 years earlier. In this sense, statistics has always existed in an era where mechanical calculation was possible. For a few thousand examples of real datasets that people were expected to analyze only with pencil and paper--using no "analytical solutions" whatsoever--please consult John Tukey's book EDA (1977). $\endgroup$ – whuber Jul 28 '18 at 18:08
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There were rooms of people known as "computers" who would do the calculations by hand, as Nick Cox stated. Apart from analytical solutions, I imagine that they could solve problems using numerical approximations based on, e.g., a few terms of a Taylor's Series expansion. Also, they had lots of tables (logs, probabilities) they could refer to.

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