Cassie's length-frequency example

Source:

Cassie, R.M. (1954). Some uses of probability paper in the analysis of size frequency distributions. Aust. J. Mar. Freshwater Res. 5 , 513-522.

The data, lengths (in) of 256 snapper (Chrysophrys auratus Forster) taken by a trawl with a mesh of about 1.5 in, are given in Table 5 of that paper. Cassie's results are given in his Table 1.

Remarks:

The components are sufficiently well separated for Cassie's probability plot method to work. MIX also works very well and gives nearly identical results. Cassie fitted normal components; the analysis here shows lognormal components.

``` Fitting Lognormal components

Proportions and their standard errors
.10547    .55808    .23919    .08411    .01315
.02089    .04105    .04662    .03219    .00991

Means and their standard errors
3.2629    5.3394    7.5594    9.6894   12.2463
.0822     .0762     .1160     .3040     .5005

Sigmas and their standard errors
.3225     .6375     .5383     .7236     .5581
.0829     .0765     .1317     .3234     .5322

Degrees of freedom = 40 - 1 +   0 -  0 - 14 -   0 =  25

Chi-squared =  12.3550            (P =  .9835)
* WARNING *  GOODNESS-OF-FIT TEST MAY BE INVALID;   7 EXPECTED COUNTS ARE < 1```
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