The post Outlier test statistics appeared first on ConsultGLP.

]]>It is quite difficult to identify suspected values visually as outliers from a set of data collected. Very often, an outlier statistic test is to be performed before further action such as deletion of such data or further testing, as we do not wish to discard such data without sound statistical justification. Read on … The outlier test statistic

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]]>In repeated chemical analysis which assumes normal probability distribution, we may find some extreme (i.e. the biggest or smallest result) is a suspect which seems to be quite different from the rest of the data set. In other words, this result does not seem to belong to the distribution of the rest of the data. This suspect value is called an outlier. Read more …. What is an outlier ?

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]]>The post Assumptions of using ANOVA appeared first on ConsultGLP.

]]>Analysis of variance (ANOVA) is useful in laboratory data analysis for significance testing. It however, has certain assumptions that must be met for the technique to be used appropriately. Their assumptions are somewhat similar to those of regression because both linear regression and ANOVA are really just two ways of analysis the data that use the general linear model. Departures from these assumptions can seriously affect inferences made from the analysis of variance.

The assumptions are:

**Appropriateness of data**

The outcome variables should be continuous, measured at the interval or ratio level, and are unbounded or valid over a wide range. The factor (group variables) should be categorical (i.e. being an object such as Analyst, Laboratory, Temperature, etc.);

**Randomness and independence**

Each value of the outcome variable is independent of each other value to avoid biases. There should not have any influence of the data collected. That means the samples of the group under comparison must be randomly and independently drawn from the population.

**Distribution**

The continuous variable is approximately *normally* distributed within each group. This distribution of the continuous variable can be checked by creating a histogram and by a statistical test for normality such as the Anderson-Darling or the Kolmogorov-Smirnov. However, the one-way ANOVA *F*-test is fairly robust against departures from the normal distribution. As long as the distributions are not extremely different from a normal distribution, the level of significance of the ANOVA *F*-test is usually not greatly affected by lack of normality, particularly for large samples.

**Homogeneity of variance**

The variance of each of the groups should be approximately equal. This assumption is needed in order to combine or pool the variances within the groups into a single within-group source of variation SSW. The Levene statistic test can be used to check variance homogeneity. The null hypothesis is that the variance is homogeneous, so if the Levene statistic are not statistically significant (normally at alpha <0.05), the variances are assumed to be sufficiently homogeneous to proceed in the data analysis.

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]]>The post The variance ratio test appeared first on ConsultGLP.

]]>*The Fisher F-test statistic is based on the ratio of two experimentally observed variance, which are squared standard deviations. Therefore, it is useful to test whether two standard deviations s _{1} and s_{2}, calculated from two independent data sets are significantly different in terms of precision from each other. * Read more …The variance ratio F-test statistic

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]]>Calculation techniques in combining uncertainties

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]]>The post What is least square difference? appeared first on ConsultGLP.

]]>Application of Least Significance Difference

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]]>The post Microbiological data transformation appeared first on ConsultGLP.

]]>The outcome of data analysis would be seriously flawed if we were to directly take the counts for statistical evaluation like what we would normally do for a set of chemical analysis data.

To overcome this, we may consider microbial growth data as being log-normally distributed to cater for the physiological or biochemical based mechanism involved.

Many microbiologists in their recovery studies would have noticed that the % recoveries can never be found satisfactory after dividing the experimental colony counts with the known inoculated number of bacteria. They tend to be in the region of 70% or so. However, once the data are logarithmic transformed to the base of 10, the relative standard deviation RSD’s obtained are more acceptable, as shown in the figure below:

Figure 2: The % recoveries of colony forming units (cfu)/ml

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]]>The post What is MAD? appeared first on ConsultGLP.

]]>MAD stands for the median absolute deviation.

It is one way to estimate the variability in a set of data, particularly when the data set has some extreme values as outliers. The general approach is to take the absolute values of deviations of individual values from a measure of their central tendency (i.e., the median of the data set).

Why do we choose to use the median instead of the arithmetic mean?

The median, by definition, is the middle value in an ordered sequence of data. Thus, it is *unaffected* by extreme values in the data set.

Therefore, we calculate the deviation of each data from the median of the original data set and then again find the median of the absolute values of these deviations, expressed as MAD. It is being used in the robust statistics.

We often use wish to use MAD as an estimator of the population standard deviation, but it cannot be adopted directly but has to be multiplied by a constant, 1.4826 first to become a *consistent* estimate of the population standard deviation.

It may be noted that an important desirable property of a statistic is consistency. A consistent statistic comes nearer to a population parameter when the size of the sample on which it is based gets larger. For example, analysis of 3 samples may give a sample mean which is much different from the expected population mean but when 30 samples are analyzed, the mean would be found much closer to the population parameter as the mean is known to be a consistent statistic.

You may wish to read our previous article https://consultglp.com/2015/02/02/robust-statistics-mad-method/ which demonstrates how the constant, 1.4826 is derived from.

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