Null Hypothesis | Zoology Optional Notes for UPSC PDF Download

Definition of Null Hypothesis

• Null hypothesis is defined as "the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact".
• More formally, we can define a null hypothesis as "a statistical theory suggesting that no statistical relationship exists between given observed variables".

Null Hypothesis in Biology

• Biology definition: A null hypothesis is an assumption or proposition where an observed difference between two samples of a statistical population is purely accidental and not due to systematic causes. It is the hypothesis to be investigated through statistical hypothesis testing so that when refuted indicates that the alternative hypothesis is true. Thus, a null hypothesis is a hypothesis that is valid or presumed true until invalidated by a statistical test. And so, one cannot say that a null hypothesis is "accepted" rather it "cannot be rejected" as it remains to be true based on the statistical evidence supporting it. Conversely, a null hypothesis that is refuted can be said to have been "rejected". Word origin: coined by the English geneticist and statistician Ronald Fisher. Symbol: H0. Compare: alternative hypothesis

Null Hypothesis vs. Alternative Hypothesis

• A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. There are two possibilities: it can be false or true.
  • For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment.
  • In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis.
    • Null Hypothesis: There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.
  • The alternate hypothesis is the reverse of the null hypothesis.
    • Alternate Hypothesis: There are statistical relationships among the forms of water that are given to plants for growth and nourishment.
  • The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.

Significance Tests

• To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population.
  • P-value = Pr(data or data more extreme | H₀ true)
  • When to reject the null hypothesis: Researchers will reject the null hypothesis if it is proven wrong after experimentation.
  • The P-value is the probability of getting a test statistic at least as extreme as the observed one.

Perceived Problems With the Null Hypothesis

• Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis.
  • The P-value has the foremost importance in the testing of the null hypothesis but as an inferential tool and for interpretation, it has a problem.
  • Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected.
  • The exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.

Null Hypothesis Examples

Example 1: Hypotheses with One Sample of One Categorical Variable

• Research Question: Do artists have a higher likelihood of being left-handed compared to the general population?
• Response Variable: Categorizing students as left-handed or right-handed.
• Null Hypothesis: Students at the College of Arts and Architecture are not more likely to be left-handed than the general population (Left-handed students at the college = 10% or p = 0.10).

Example 2: Hypotheses with One Sample of One Measurement Variable

• Research Question: Does the average dosage of a generic brand of antihistamine differ from the specified 50mg dosage?
• Response Variable: Measuring the dosage of the active ingredient.
• Null Hypothesis: The average dosage of capsules from this brand is usually 50mg (population average dosage = 50mg).

Example 3: Hypotheses with Two Samples of One Categorical Variable

• Research Question: Does the data suggest that females prefer vegetarian meals more than males?
• Response Variable: Categorizing individuals into vegetarian and non-vegetarian groups.
• Grouping Variable: Gender
• Null Hypothesis: Gender is not associated with preference for vegetarian meals (population percentage of women who prefer vegetarian meals = population percentage of men who prefer vegetarian meals or p women = p men).

Example 4: Hypotheses with Two Samples of One Measurement Variable

• Research Question: Does a low-carbohydrate diet lead to faster weight loss than a low-fat diet?
• Response Variable: Weight loss (in pounds).
• Explanatory Variable: Type of diet (low carbohydrate or low fat).
• Null Hypothesis: There is no significant difference in mean weight loss between people on a low-carbohydrate diet and people on a low-fat diet (population mean weight loss on a low-carbohydrate diet = population mean weight loss on a low-fat diet).

Example 5: Hypotheses about the relationship between Two Categorical Variables

• Research Question: Does exposure to second-hand smoke increase the risk of stroke?
• Variables: Two categories of variables (controls and stroke patients) and (living with a smoker). The odds of having a stroke are influenced by living with a smoker.
• Null Hypothesis: There is no significant relationship between exposure to passive smoke and stroke (odds ratio between stroke and passive smoke exposure is equal to 1).