Hypothesis testing is as old as the scientific method and is at the heart of the research process.
Research exists to validate or disprove assumptions about various phenomena. The process of validation involves testing and it is in this context that we will explore hypothesis testing.
A hypothesis is a calculated prediction or assumption about a population parameter based on limited evidence. The whole idea behind hypothesis formulation is testing—this means the researcher subjects his or her calculated assumption to a series of evaluations to know whether they are true or false.
Typically, every research starts with a hypothesis—the investigator makes a claim and experiments to prove that this claim is true or false. For instance, if you predict that students who drink milk before class perform better than those who don't, then this becomes a hypothesis that can be confirmed or refuted using an experiment.
Also known as a basic hypothesis, a simple hypothesis suggests that an independent variable is responsible for a corresponding dependent variable. In other words, an occurrence of the independent variable inevitably leads to an occurrence of the dependent variable.
Typically, simple hypotheses are considered as generally true, and they establish a causal relationship between two variables.
Examples of Simple Hypothesis
A complex hypothesis is also known as a modal. It accounts for the causal relationship between two independent variables and the resulting dependent variables. This means that the combination of the independent variables leads to the occurrence of the dependent variables.
Examples of Complex Hypotheses
As the name suggests, a null hypothesis is formed when a researcher suspects that there's no relationship between the variables in an observation. In this case, the purpose of the research is to approve or disapprove this assumption.
Examples of Null Hypothesis
To disapprove a null hypothesis, the researcher has to come up with an opposite assumption—this assumption is known as the alternative hypothesis. This means if the null hypothesis says that A is false, the alternative hypothesis assumes that A is true.
An alternative hypothesis can be directional or non-directional depending on the direction of the difference. A directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than the null value while a non-directional hypothesis only validates the existence of a difference without stating its direction.
Examples of Alternative Hypotheses
Logical hypotheses are some of the most common types of calculated assumptions in systematic investigations. It is an attempt to use your reasoning to connect different pieces in research and build a theory using little evidence. In this case, the researcher uses any data available to him, to form a plausible assumption that can be tested.
Examples of Logical Hypothesis
After forming a logical hypothesis, the next step is to create an empirical or working hypothesis. At this stage, your logical hypothesis undergoes systematic testing to prove or disprove the assumption. An empirical hypothesis is subject to several variables that can trigger changes and lead to specific outcomes.
Examples of Empirical Testing
When forming a statistical hypothesis, the researcher examines the portion of a population of interest and makes a calculated assumption based on the data from this sample. A statistical hypothesis is most common with systematic investigations involving a large target audience. Here, it's impossible to collect responses from every member of the population so you have to depend on data from your sample and extrapolate the results to the wider population.
Examples of Statistical Hypothesis
Hypothesis testing is an assessment method that allows researchers to determine the plausibility of a hypothesis. It involves testing an assumption about a specific population parameter to know whether it's true or false. These population parameters include variance, standard deviation, and median.
Typically, hypothesis testing starts with developing a null hypothesis and then performing several tests that support or reject the null hypothesis. The researcher uses test statistics to compare the association or relationship between two or more variables.
Researchers also use hypothesis testing to calculate the coefficient of variation and determine if the regression relationship and the correlation coefficient are statistically significant.
The basis of hypothesis testing is to examine and analyze the null hypothesis and alternative hypothesis to know which one is the most plausible assumption. Since both assumptions are mutually exclusive, only one can be true. In other words, the occurrence of a null hypothesis destroys the chances of the alternative coming to life, and vice-versa.
To successfully confirm or refute an assumption, the researcher goes through five (5) stages of hypothesis testing;
Like we mentioned earlier, hypothesis testing starts with creating a null hypothesis which stands as an assumption that a certain statement is false or implausible. For example, the null hypothesis (H0) could suggest that different subgroups in the research population react to a variable in the same way.
Once you know the variables for the null hypothesis, the next step is to determine the alternative hypothesis. The alternative hypothesis counters the null assumption by suggesting the statement or assertion is true. Depending on the purpose of your research, the alternative hypothesis can be one-sided or two-sided.
Using the example we established earlier, the alternative hypothesis may argue that the different sub-groups react differently to the same variable based on several internal and external factors.
Many researchers create a 5% allowance for accepting the value of an alternative hypothesis, even if the value is untrue. This means that there is a 0.05 chance that one would go with the value of the alternative hypothesis, despite the truth of the null hypothesis.
Something to note here is that the smaller the significance level, the greater the burden of proof needed to reject the null hypothesis and support the alternative hypothesis.
Test statistics in hypothesis testing allow you to compare different groups between variables while the p-value accounts for the probability of obtaining sample statistics if your null hypothesis is true. In this case, your test statistics can be the mean, median and similar parameters.
If your p-value is 0.65, for example, then it means that the variable in your hypothesis will happen 65 in100 times by pure chance. Use this formula to determine the p-value for your data:
After conducting a series of tests, you should be able to agree or refute the hypothesis based on feedback and insights from your sample data.
Hypothesis testing isn't only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine.
In a factory or other manufacturing plants, hypothesis testing is an important part of quality and production control before the final products are approved and sent out to the consumer.
During ideation and strategy development, C-level executives use hypothesis testing to evaluate their theories and assumptions before any form of implementation. For example, they could leverage hypothesis testing to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales.
In addition, hypothesis testing is used during clinical trials to prove the efficacy of a drug or new medical method before its approval for widespread human usage.
An employer claims that her workers are of above-average intelligence. She takes a random sample of 20 of them and gets the following results:
Mean IQ Scores: 110
Standard Deviation: 15
Mean Population IQ: 100
Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.
Step 2: State that the alternative hypothesis is greater than 100.
Step 3: State the alpha level as 0.05 or 5%
Step 4: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.
Step 5: Calculate the test statistics using this formula
Z = (110–100) ÷ (15÷√20)
10 ÷ 3.35 = 2.99
If the value of the test statistics is higher than the value of the rejection region, then you should reject the null hypothesis. If it is less, then you cannot reject the null.
In this case, 2.99 > 1.645 so we reject the null.
The most significant benefit of hypothesis testing is it allows you to evaluate the strength of your claim or assumption before implementing it in your data set. Also, hypothesis testing is the only valid method to prove that something "is or is not". Other benefits include:
Several limitations of hypothesis testing can affect the quality of data you get from this process. Some of these limitations include:
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