Statistical methods in food and consumer research pdf

Therefore, it is useful when it is difficult to measure the values. Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums. It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

The two-sample Kolmogorov-Smirnov KS test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

The Kruskal—Wallis test is a non-parametric test to analyse the variance. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic. In contrast to Kruskal—Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal—Wallis test. The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups i.

It is calculated by the sum of the squared difference between observed O and the expected E data or the deviation, d divided by the expected data by the following formula:. A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables.

It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data.

The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used. Numerous statistical software systems are available currently. There are a number of web resources which are related to statistical power analyses.

A few are:. It gives an output of a complete report on the computer screen which can be cut and paste into another document. It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article.

Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

National Center for Biotechnology Information , U. Journal List Indian J Anaesth v. Indian J Anaesth. Zulfiqar Ali and S Bala Bhaskar 1. Author information Copyright and License information Disclaimer. Address for correspondence: Dr. E-mail: moc. This article has been corrected. See Indian J Anaesth. This article has been cited by other articles in PMC. Abstract Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings.

Key words: Basic statistical tools, degree of dispersion, measures of central tendency, parametric tests and non-parametric tests, variables, variance. Open in a separate window. Figure 1. Quantitative variables Quantitative or numerical data are subdivided into discrete and continuous measurements. Table 1 Example of descriptive and inferential statistics. Descriptive statistics The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency The measures of central tendency are mean, median and mode. The variance of a sample is defined by slightly different formula: where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample.

The SD of a sample is defined by slightly different formula: where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. Table 2 Example of mean, variance, standard deviation. Normal distribution or Gaussian distribution Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.

Figure 2. Skewed distribution It is a distribution with an asymmetry of the variables about its mean. Figure 3. Curves showing negatively skewed and positively skewed distribution.

Inferential statistics In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population.

Table 3 P values with interpretation. Table 4 Illustration for null hypothesis. Parametric tests The parametric tests assume that the data are on a quantitative numerical scale, with a normal distribution of the underlying population.

Student's t -test Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. The formula for paired t -test is: where d is the mean difference and SE denotes the standard error of this difference.

Analysis of variance The Student's t -test cannot be used for comparison of three or more groups. A simplified formula for the F statistic is: where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Non-parametric tests When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Table 5 Analogue of parametric and non-parametric tests. Tests to analyse the categorical data Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. It is calculated by the sum of the squared difference between observed O and the expected E data or the deviation, d divided by the expected data by the following formula: A Yates correction factor is used when the sample size is small.

A few are: StatPages. Financial support and sponsorship Nil. Huang, J. Journal of Food Engineering , , — Author : R. Author : Abbas F. R statistical software is used throughout the book to analyze the data. Author : Mohammed M. Crampin, E. Pattern formation in reaction—diffusion models with nonuniform domain growth. Add to cart. Sales tax will be calculated at check-out. Resources Textbook Support for Instructors. Free Global Shipping. Description Statistical Methods in Food and Consumer Research, Second Edition, continues to be the only book to focus solely on the statistical techniques used in sensory testing of foods, pharmaceuticals, cosmetics, and other consumer products.

This new edition includes the most recent applications of statistical methods, and features significant updates as well as two new chapters.