In today’s data-driven world, decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.
Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.
Let's discuss few examples of statistical hypothesis from real-life -
Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.
Z = ( x̅ – μ0 ) / (σ /√n)
An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.
The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.
The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.
H0 is the symbol for it, and it is pronounced H-naught.
The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.
Let's understand this with an example.
A sanitizer manufacturer claims that its product kills 95 percent of germs on average.
To put this company's claim to the test, create a null and alternate hypothesis.
H0 (Null Hypothesis): Average = 95%.
Alternative Hypothesis (H1): The average is less than 95%.
Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.
Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.
To calculate the z-score, we would use the following formula:
z = ( x̅ – μ0 ) / (σ /√n)
z = (5'5" - 5'4") / (2" / √100)
We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".
Hypothesis testing is a statistical method to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here’s a breakdown of the typical steps involved in hypothesis testing:
The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. Common choices for α are 0.05 (5%), 0.01 (1%), and 0.10 (10%).
Choose a statistical test based on the type of data and the hypothesis. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis. The selection depends on data type, distribution, sample size, and whether the hypothesis is one-tailed or two-tailed.
Gather the data that will be analyzed in the test. This data should be representative of the population to infer conclusions accurately.
Based on the collected data and the chosen test, calculate a test statistic that reflects how much the observed data deviates from the null hypothesis.
The p-value is the probability of observing test results at least as extreme as the results observed, assuming the null hypothesis is correct. It helps determine the strength of the evidence against the null hypothesis.
Compare the p-value to the chosen significance level:
Present the findings from the hypothesis test, including the test statistic, p-value, and the conclusion about the hypotheses.
Depending on the results and the study design, further analysis may be needed to explore the data more deeply or to address multiple comparisons if several hypotheses were tested simultaneously.
To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.
A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.
You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.
Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.
Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.
A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.
Become a Data Scientist through hands-on learning with hackathons, masterclasses, webinars, and Ask-Me-Anything! Start learning now!
Depending on the population distribution, you can classify the statistical hypothesis into two types.
Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.
Composite Hypothesis: A composite hypothesis specifies a range of values.
A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.
Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.
The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.
In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.
In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.
If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.
If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):
The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.
Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "
Suppose H0: mean = 50 and H1: mean not equal to 50
According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.
In a similar manner, if H0: mean >=50, then H1: mean
Here the mean is less than 50. It is called a One-tailed test.
A hypothesis test can result in two types of errors.
Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.
Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.
Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.
H0: Student has passed
H1: Student has failed
Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true].
Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].
Our Data Scientist Master's Program covers core topics such as R, Python, Machine Learning, Tableau, Hadoop, and Spark. Get started on your journey today!
Hypothesis testing has some limitations that researchers should be aware of:
After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science. The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.
If you are interested in statistics of data science and skills needed for such a career, you ought to explore the Post Graduate Program in Data Science.
If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!
Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.
In statistics, H0 and H1 represent the null and alternative hypotheses. The null hypothesis, H0, is the default assumption that no effect or difference exists between groups or conditions. The alternative hypothesis, H1, is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data.
A simple hypothesis is a specific statement predicting a single relationship between two variables. It posits a direct and uncomplicated outcome. For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here, the hypothesis suggests a direct relationship between the amount of sunlight (independent variable) and the growth rate of sunflowers (dependent variable), with no additional variables considered.
The three major types of hypotheses are:
| Name | Date | Place | |
|---|---|---|---|
| PL-300 Microsoft Power BI Certification Training | 21 Sep -6 Oct 2024, Weekend batch | Your City | View Details |
| PL-300 Microsoft Power BI Certification Training | 12 Oct -27 Oct 2024, Weekend batch | Your City | View Details |
| PL-300 Microsoft Power BI Certification Training | 26 Oct -10 Nov 2024, Weekend batch | Your City | View Details |
Avijeet Biswal
Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.
