--------------------------------------------------------------------------------
6 BASIC STATISTICAL TOOLS
There are lies, damn lies, and statistics......
(Anon.)
--------------------------------------------------------------------------------
6.1 Introduction
6.2 Definitions
6.3 Basic Statistics
6.4 Statistical tests
--------------------------------------------------------------------------------
6.1 Introduction
In the preceding chapters basic elements for the proper execution of analytical work such as personnel, laboratory facilities, equipment, and reagents were discussed. Before embarking upon the actual analytical work, however, one more tool for the quality assurance of the work must be dealt with: the
…show more content…
It is constituted by a combination of random and systematic errors (precision and bias) and cannot be quantified directly. The test result may be a mean of several values. An accurate determination produces a "true" quantitative value, i.e. it is precise and free of bias.
6.2.3 Precision
The closeness with which results of replicate analyses of a sample agree. It is a measure of dispersion or scattering around the mean value and usually expressed in terms of standard deviation, standard error or a range (difference between the highest and the lowest result).
6.2.4 Bias
The consistent deviation of analytical results from the "true" value caused by systematic errors in a procedure. Bias is the opposite but most used measure for "trueness" which is the agreement of the mean of analytical results with the true value, i.e. excluding the contribution of randomness represented in precision. There are several components contributing to bias:
1. Method bias
The difference between the (mean) test result obtained from a number of laboratories using the same method and an accepted reference value. The method bias may depend on the analyte level.
2. Laboratory bias
The difference between the (mean) test result from a particular laboratory and the accepted reference value.
3. Sample bias
The difference between the mean of replicate test results of a sample and the ("true") value of the target population from which the sample was
For example, we could calculate the IQ difference for each subject by subtracting their IQ while taking a placebo from their IQ while taking the new drug. If our sample average was positive, it would mean that, on average, our subjects had a higher IQ while they were taking the experimental drug than they had while taking the placebo.
Theoretically from the recorded data the calculated mean, median, and mode will be the most accurate representation of the real world value. The difference between the highest recorded value and lowest recorded value is the range in the set of data. Standard deviation (s) is a quantity calculated to indicate an extend of deviation for a group of data as a whole (Marshall). This is calculated using:
Research results tell us information about data that has been collected. Within the data results, the author states the results are statistically significant, meaning that there is a relationship within either a positive and negative correlation. The M (Mean) of the data tells the average value of the results. The (SD) Standard Deviation is the variability of a set of data around the mean value in a distribution (Rosnow & Rosenthal, 2013).
Answer: The standard deviation is a measure of spread in a continuous variable. When the variable is
Examples are the determination of physical constants such as melting point, boiling point, or density, and instrumental techniques such as infrared (IR) spectroscopy. Sometimes these techniques are referred to as analytical techniques. LAB REPORTS FOR CHEMICAL PREPARATIONS, OR SYNTHESIS This type of report refers to experiments whose main goal is to prepare a pure substance from specific starting materials. This necessarily involves a chemical transformation, or reaction. In the simplest case, there is only one step. The starting materials are combined and a product forms. This product is isolated, purified, and characterized, producing the final outcome of the experiment. In a multistep synthesis, the product of the first step is used as a starting material in a second step, and so on, until a final product is obtained. No multistep syntheses are performed in organic lab I. Some two step syntheses are performed in organic lab II.
The analytical balance measures to the ten thousandths place meaning those measurements could have 4 to 6 significant
3) Compute limits for the sample mean X around μ=12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satifactorily. If X exceeds the upper limit or if X is below the lower limit, corrective action will be taken. These limits are refferred to as upper and lower control limits fro quality control purposes.
Percent error for sample C was 0.342% on the double pan balance, 0.104% on the electronic scale, and 0.00556% on the analytical balance. For sample G, percent error was 0.281% on the double pan balance, 0.141% on the electronic balance, and 0.001671% on the analytical balance. The percent error calculations for sample 6 were 1.24% on the double pan balance and 0.00868% for both the electronic balance and the analytical balance.
a type of error in research that is made by the person doing the research that changes or misleads the research findings.
and the number of False Negatives. In another way it is the number of positive
Just like the central tendency, there are three measures of variability: range, standard deviation and the variance.
The BSA standard solution concentration for test tubes 10 and 11 was found to be 1.2 mg/mL, and 1 mg/mL and 0.9 mg/mL for test tubes 8 and 9 respectively. Results for
If an experiment contains biological error or systematic errors, they must be considered in addition to the statistical error in order to completely analyze the data.
A confidence interval is a range within which most probable values would occur around a measurement. They are used to convey how correct an estimate of the population is, based on the sample size. By using the traditional normal based method to calculate the C.I, the degree of confidence that the population is within the range is measured as a probability; in this case 95% and 99%.
The distribution of the test statistic under the null-hypothesis is derived from the assumptions identified previously. Common test statistics may follow the following distributions: Normal, Student T, and Chi-Square. This distribution separates the possible values of the estimator into two categories: values for which the null-hypothesis is accepted or rejected. The region for which we accept the null-hypothesis is called the critical region and the area underneath the curve that corresponds to the critical region is known as the level of confidence. Hence, we can develop a confidence interval for which we can see the lowest and highest point of the critical region. Any observed sample mean that lies outside of this confidence interval (outside the critical region) would cause us to reject the null-hypothesis in favor of the alternative hypothesis. The area of the rejection region is known as the level of significance and represents type I error (alpha) corresponding to the probability that a true null-hypothesis is rejected (as opposed to type II error- beta; the probability of accepting a false null-hypothesis). Essentially, hypothesis testing calls for comparing a test statistic to the critical value of the test statistic. If this test statistic is greater than the critical value of the test statistic, we will reject the null hypothesis in favor of the alternative hypothesis. If