Hypothesis

 What is a hypothesis? 

A hypothesis is a supposition made as a basis for reasoning. The first thing in hypothesis testing is to set up a hypothesis about a population parameter. Then we collect sample data, produce sample statistics, and use this information to decide how likely it is that our hypothesized population parameter is correct. A hypothesis is a testable and falsifiable statement or educated guess that proposes a tentative explanation for a phenomenon, event, or observation. In the scientific method, hypotheses are formulated as a fundamental step in the process of conducting research, experimentation, or investigation to understand, explain, or predict various natural, social, or empirical phenomena. Hypotheses serve as the foundation for designing experiments, collecting data, and drawing conclusions in scientific inquiry. Here are the key characteristics and components of the hypotheses:

Testability: A hypothesis must be framed in a way that it can be tested through empirical observation or experimentation. It should be possible to gather evidence that either supports or refutes the hypothesis.

Falsifiability: A good scientific hypothesis is falsifiable, meaning there must be a way to demonstrate that it is false. If a hypothesis cannot be disproven, it is not considered scientifically valid. Falsifiability is an essential criterion to distinguish scientific hypotheses from non-scientific statements or beliefs.

Clear and Specific: A hypothesis should be clear and specific in its statement. It should define the variables or factors being studied and the expected relationship between them.

Based on Existing Knowledge: Hypotheses are often formulated based on prior knowledge, existing theories, or observations. They represent a logical extension of what is already known or a new perspective on a phenomenon.

Predictive: Hypotheses make predictions about the outcomes of experiments or observations. They provide a framework for understanding how changes in one variable may affect another.

Alternative Hypotheses: In hypothesis testing, there are typically two types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the default or no-effect scenario, while the alternative hypothesis represents the researcher's proposed explanation or effect.

Example: Here is an example of a scientific hypothesis: "Increasing the amount of sunlight a plant receives will result in faster growth compared to plants receiving less sunlight." In this hypothesis, the independent variable is the amount of sunlight, the dependent variable is plant growth, and the hypothesis makes a specific prediction about the relationship between these variables.

Hypothesis Testing: Once a hypothesis is formulated and data is collected, statistical techniques are often used to test whether the evidence supports or refutes the hypothesis. The results of hypothesis testing help researchers draw conclusions and make inferences about the phenomenon being studied.

Revisions and Iteration: Hypotheses can be revised or refined based on the results of experiments or observations. If evidence contradicts the initial hypothesis, researchers may modify their hypothesis and conduct further research.

Hypotheses play a fundamental role in scientific research by guiding the scientific process, enabling researchers to formulate questions, design experiments, and draw meaningful conclusions. They are a critical component of the scientific method, helping to advance our understanding of the natural world and solve complex problems in various fields of study.

hypothesis concept

Concept of Hypothesis

A hypothesis in statistics is simply a quantitative statement about a population. We collect sample data, produce sample statistics, and use this information to decide how likely it is that our hypothesized population parameter is correct. For example, a coin may be tossed 200 times and we may get heads 90 times and tails 110 times, we may now be interested in testing the hypothesis that the coin is unbiased.
The two hypotheses in a statistical test are normally referred to as:
a) Null Hypothesis 
b) Alternative Hypothesis
Null Hypothesis:
The null hypothesis is a very useful tool in testing the significance of the difference. The null hypothesis is akin to the legal principle that a man is innocent until he is proven guilty.
Alternative Hypothesis:
The alternate hypothesis specifies those values that the researcher believes to hold true and of course, he hopes that the sample data lead to acceptance of this hypothesis as true. The alternative hypothesis may embrace the whole range of values rather than a single point.

Difference between  null and alternative hypothesis

The null and alternative hypotheses are distinguished by the use of two different symbols H(0) representing the null hypothesis and H(a) the alternative hypothesis. Thus a psychologist who wishes to test whether or not a certain class of people has a mean I.Q. higher than 100 might establish the null and alternative hypothesis:
H(0) = mu = 100(null hypothesis)
H(a) = mu not equal 100 (alternative hypothesis)
If a researcher is interested in testing the difference between the mean I.Q.of  two groups, this psychologist may like to establish the null hypothesis that two groups have equal means(mu1-mu2 =0) and the alternative hypothesis that their means are not equal (mu1-mu2 is not equal 0).
H(0) = mu1 -  mu2=0(null hypothesis)
H(a) = mu1 -mu2 not equal to 0 (alternative hypothesis)

Type I and Type II Errors

When a statistical hypothesis  is tested there are four possibilities:
1) The hypothesis is true but our test rejects it (Type I error)
2) The hypothesis is false but our test accepts it (Type II error)
3) The hypothesis is true  and our test accepts it (Correct decision)
4) The hypothesis  is false  and our test rejects it (Correct decision)

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