Role of Statistics in Scientific Research

Editor's Notes

• #23: Population sampling As we discussed in previous discussion sessions, population sampling can be defined as the procedure of taking a subset of larger population. Inferential statistics seek to make predictions about a population based on the results observed in a sample of that population. Generalization Generalization is the attempt to extend the results of a sample to a population. When generalizing, sample variation must be taken into account. Even if the sample selection is completely random, still there is a degree of variance within the population. The concept 'margin of error' comes into the field due to this reason. Hypothesis A quantitative research process starts with a hypothesis, and the research design is based on this hypothesis. Hypothesis is defined as a proposed explanation for a phenomenon. A well designed research disproves the null hypothesis. Significance tests Significance tests are used to determine the probability of the research result if the null hypothesis was true. p-value is used to determine this probability statistically. Correlation When two variables move together, they are said to be correlated. Correlation can be either positive where one variable rises, the other variable rises as well or negative where two variables move in opposite directions. Regression analysis Regression analysis is used to determine if there is or isn’t a correlation between two or more variables and how strong any correlation may be. It involves plotting data points on an X/Y graph and looking at the distribution of data it establishes a trend line. Correlation coefficient (r) Correlation coefficient is used to indicate the degree to which two quantitative variables are related. The most common Correlation coefficient which is used is the Pearson coefficient. Causation Causation or cause and effect relationship denotes when one variable changes another. Unlike in correlation relationship, causation flows on only one direction.   Dependent and Independent variable In a causation relationship, the factor that drives change is the independent variable. The variable that is driven is the dependent variable. Elasticity Elasticity is mainly used in economics research. It measures how much a change in one variable affects another. Standard deviation Standard deviation measures the difference from the group's mean to provide an insight of much variation there is within a group of values. Dependent t-test A data analysis procedure that assesses whether the means of two related groups are statistically different from each other. t-Test The t- test is used to calculate the confidence intervals of a measurement when the population standard deviation is not know. The t-test is also used to compare two averages. The t-test corrects for the uncertainty of the sample standard deviation (s) caused by taking a small number of samples. Q-Test This test is used to determine if there is a statistical basis for removing a data point from a data set. The t-test enables to see whether two samples are different when you have data that are continuous and normally distributed. The test allows comparing the means and standard deviations of the two groups to see whether there is a statistically significant difference between them. Chi-squared test The chi-squared test is used with categorical data to see whether any difference in frequencies between sets of results is due to chance. The chi-square test assumes the expected value of each cell is five or higher.  Mann–Whitney U-test The Mann–Whitney U-test is similar to the t-test. It is used when comparing ordinal data that are not normally distributed. Measurements must be categorical, yes or no and independent of each other. The Mann–Whitney U-test could be used to test the effectiveness of an antihistamine tablet compared to a spray in a group of people with hay fever. To do this, you would split the group in half, then give each half a different treatment and ask each person how effective they thought it was. The test could be used to see whether there is a difference in the perceived efficacy of the two treatments. Standard error and 95 per cent confidence limits The standard error and 95 per cent confidence limits allow us to gauge how representative of the real world population the data are. Spearman’s rank correlation coefficient The Spearman’s rank correlation coefficient tests the relationship between two variables in a dataset; for example, is a person’s weight related to their height? If there is a statistically significant relationship, you can reject the null hypothesis, which may be that there is no link between the two variables. Wilcoxon matched pairs test Like the Mann–Whitney U-test, this test is used for discontinuous data that are not normally distributed but do have a link between the two datasets. For example, when asking people to rank how hungry they feel before a meal and doing so again after they have eaten because the same person is providing both answers, the datasets are not independent. Fisher's exact test The Fisher's exact test is used when you want to conduct a chi-square test, but one or more of your cells has an expected frequency of five or less.  Remember that the chi-square test assumes that each cell has an expected frequency of five or more, but the Fisher's exact test has no such assumption and can be used regardless of how small the expected frequency is. One-way ANOVA A one-way analysis of variance (ANOVA) is used when you have a categorical independent variable with two or more categories and a normally distributed interval dependent variable and you wish to test for differences in the means of the dependent variable broken down by the levels of the independent variable. 
• #25: Discarding unfavorable data This is a main misuse happen in the research. Researchers tend to discard the unfavorable data to their research study Loaded questions The answers to surveys can often be manipulated by wording the question in such a way as to induce a prevalence towards a certain answer from the respondent. For example, in polling support for a war, the questions: Do you support the attempt by the USA to bring freedom and democracy to other places in the world? Do you support the unprovoked military action by the USA? Overgeneralization Overgeneralization is a fallacy occurring when a statistic about a particular population is asserted to hold among members of a group for which the original population is not a representative sample. False causality he fallacy is that an event or action influences another that is not reasonably related. Ex.: "There were many strangers in the room, so naturally they began to argue." Suspect Samples "Three out of four doctors surveyed recommend brand Misleadatron."  If  only 4 doctors were surveyed, the results could have been obtained by  chance alone; however, if 100 doctors were surveyed, the results might  be quite different. But probably not the desired one. Ambiguous Averages "There are four commonly used measures that are loosely called averages. They are the mean, median, mode, and midrange." For the same data set, these averages can differ markedly. People who  know this can, without lying, select the one measure of average that  lends the most evidence to support their position.