## 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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