Basic Concept of Hypothesis Testing and Parametric Test

Abstract

Statistical analysis is done by many ways, but the majority of biologists use the ‘classical’ statistics which involves testing of null hypothesis using experimental data. In this process we estimate the probability that is obtained from the observed results or, something more extreme, if the null hypothesis is true. If the estimated probability (the p-value) is lesser than the significance value, we conclude that null hypothesis is unlikely true, and we reject the null hypothesis. So, hypothesis is defined as an assumption about a single population or about the relationship between two or more populations. It is testable and provides a possible explanation of a certain phenomenon or event. On the other hand, if a hypothesis is not testable, then it implies insufficient evidence to provide more than a tentative explanation, e.g. extinction of inland fishes. To test the new information or knowledge or belief about the populations against the existing one, two hypotheses are used, the null hypothesis (H₀) and the alternative hypothesis (H₁). Null hypothesis (H₀) assumes that there is no difference between the new and existing populations. However there can be some indications that existing knowledge of beliefs may not be true. The null hypothesis (H₀) is tested against the alternative hypothesis (H₁). The alternative hypothesis states the statistical statement indicating the presence of an effect or a difference and sometimes known as ‘an intelligent guess’ based on limited information. It may so happen that the experimental results may match predictions, but it should be believed after proper testing and analysis of appropriate statistical tool(s), which includes designing an experiment or survey to generate or collect data/information (raw), exploratory data analysis and choosing an appropriate significance level or confidence limits (intervals).

Exercise

• 1. A random sample of 30 fishes from a particular species showed an average length of 8.2 cm. Can you conclude that this has been drawn from a population with mean 8.1 cm and standard deviation 0.25 cm at 1% level of significance?

• 2. A total of 1250 fishes were taken at random from a pond, and their mean length was 9.95 cm with a standard deviation of 7.81 cm. Calculate an approximate 95% confidence interval for the mean length of the fishes.

• 3. In a particular water body, the long-term proportion of catla caught in the total catch is 51.46%. In a random sample of 5000 fishes caught from the same water body, the proportion of catla was 52.55%. Determine whether those two proportions differ significantly at 10% level or not.

• 4. The price of an aquarium fish feed at a national store is Rs. 179. A person has purchased the same feed at an online auction site for the following prices 155, 179, 175, 175 and 161 rupees. Determine (at 1% level of significance) whether the average price of the aquarium fish feed is than Rs. 179 if purchased at an online auction. Assume that the auction prices of fish feeds are normally distributed.

• 5. A group of 20 fishery graduate students were assessed by a test before and after a training programme. Their pre-test and post-test scores were recorded. The mean and standard deviation of the differences were 2.05 and 2.837, respectively. Assuming that the differences are normally distributed, can we conclude that the training improved the knowledge level of students.

• 6. A random sample of 15 fishes taken from a pond showed a mean length of 68.4 cm with a standard deviation of 16.47. A sample of 12 fishes taken from the same pond had a mean length of 83.42 cm and standard deviation of 17.63 cm. Can we conclude that there is no difference between the two means?

• 7. Failing to reject null hypothesis when it is false is

  • (a) α

  • (b) Type I error

  • (c) Type II error

  • (d) β

• 8. A ‘statistic’ is

  • (a) A sample characteristic

  • (b) A population characteristic

  • (c) Unknown

  • (d) Normally distributed

• 9. What is ‘standard normal variate’?

• 10. What is the ‘power’ in hypothesis testing?