### Methods used to analyse structural timber test data

Once a representative sample of the general structural product quality has been gathered (refer to the earlier posted article on *Sampling*), and then tested (refer to earlier posted article on *Compliance Test Methods*), the next step to consider is which method of deriving the structural properties should be used.

The use of statistics is required to ascertain the lower 5^{th} percentile values for the tested sample, from which the strength properties are based. There are 3 main statistical analysis options;

Each analysis option will give slightly different estimations of the lower 5^{th} percentile value, so it is important to fit the assumed distribution to the data and visually check its fit to the test data. These 3 methods estimating the lower 5^{th} percentile were used on the same strength test data, which has been ranked in ascending order and plotted above.

#### Non-parametric (Data)

This method is highly dependent on the size of the sample and how representative it is of the overall production quality. The lower 5^{th} percentile value is read off a plot of the ranked strength test values against the cumulative frequency, f = (i-0.5)/N; where i is ranked value (lowest = 1) and N is the sample size. The cumulative frequency plot of the ranked strength values is seldom a smooth curve, and the sample may under or over estimate the value of the lower 5^{th} percentile strength value of the general timber resource.

#### Log-Normal

This is an assumed distribution using the mean and co-efficient of variation of all the strength test data to estimate the lower 5^{th} percentile strength value. This distribution is generally favoured because of its good fit across the entire strength data set, and tends to give a slightly conservative estimate of the lower 5^{th} percentile strength value, refer to the charts above.

#### 2P Weibull

This is another assumed distribution and uses the co-efficient of variation of the lower tail of the strength test data to very accurately estimate the lower 5^{th} percentile strength value with a small sample size. This method of estimating the lower 5^{th} percentile value is best used when there is a high degree of confidence that the sample well represents the timber quality. reflects the general on material with lower variability.