Hypothesis Testing Course Overview

    Overview

    Hypothesis testing is one of the most pivotal concepts in statistics with many real-life applications. It is used by researchers all over the world to test new theories before implementing them. It helps different companies set a baseline quality of their product and decide on improvements. 


    There are a lot of different parts of testing a hypothesis, from creating a statistical statement to calculations. Nowadays, most of the work in this field is done using software like python, Minitab, SQL, or R. 


    Apart from using software, testing problems can also be solved by hand, though the process would be time-consuming and tedious. 

    What is hypothesis testing?

    Simply put, hypothesis testing is a process of examination of claims made against a process with the help of observed data. The process can be anything and is not related to only statistical problems.


    Consider a set of random variables X1,X2, X3, ..., XN

    Let F denote the distribution function of the set of random variables. 

    Note that F is chosen to keep with the experiment’s model belonging to a family of distributions


    Now, the above problem would fall under the umbrella of hypothesis testing if a suggestion of the form 

    H0 : F 0

    is encountered, where 0 is a specified proper subset of


    A statistical hypothesis is a statement used to examine the validity of claims made about the distributions of a set of random variables. The examination process is performed based on a set of observations on the random variable. 


    The process of examination of the above claims is known as hypothesis testing.


    Definition:

    If a hypothesis H0 (taken together with the model) specifies the joint distribution of X1,X2, X3, ..., Xn completely, then it is known as a simple hypothesis. 


    If H0 does not specify the joint distribution completely, it is said to be a composite hypothesis. 


    Parametric Setup


    A problem of hypothesis testing falls under a parametric setup if it is assumed that the distribution function F belonging to the set of random variables X1,X2, X3, ..., Xn is known (usually assumed to follow a Normal distribution) except for some parameter or parameters

    Non-parametric Setup


    A non-parametric setup is used for testing a hypothesis when the assumption of normality is violated. The different tests, like the t-test and f-test, work efficiently when the random variables follow a normal distribution. But for non-normal distributions, these methods are sub-optimum.

    Another term used to define a non-parametric setup is distribution-free because the procedures used for testing under this case do not depend on the distribution of the random variables.

    How does it help us determine if we can reject a null hypothesis?


    Null Hypothesis


    In a testing problem, the statistical hypothesis statement that equates to two or more possible outcomes of the experiment is known as a null hypothesis. It is usually taken to be the observed difference between the testing parameters. 

    It is denoted by H0.


    Example:

    Consider a testing problem where it is required to test if the mean of a particular distribution, indicated by F (say), acquires a specific value 0 (say). If denotes the mean of the distribution, the null hypothesis will be - 

    H0 : =0


    Alternative Hypothesis


    An alternative or alternate hypothesis is proposed in a testing problem to counter the null hypothesis. If the data from the experiment contradicts the null hypothesis, the alternate hypothesis is suggested as another option. 


    It is generally represented by H1 or Ha.


    Example:

    Consider a testing problem where it is required to test if the mean of a particular distribution, indicated by F (say), acquires a specific value 0 (say). If denotes the mean of the distribution, the null hypothesis will be - 

    H0 : =0


    Now, if the data obtained contradicts H0, then it gets rejected by the experimenter, and the alternate hypothesis gets accepted, denoted by -

    H1 : 0 


    The testing problem is usually written as


    To test - H0 : =0against H1 : 0


    The alternate hypothesis can also be of the form - 

    H1 : <0 or H1 : > 0


    Rejection or acceptance of a null hypothesis

    A null hypothesis is rejected or accepted based on the data collected by the experimenter. 


    Consider the following testing problem:


    Let X1,X2, X3, ..., Xn be a set of random variables independently and identically distributed following a normal distribution with mean and standard deviation 0, where the value of 0 is known. 


    To test: H0 : =against H1 : 0

    Where the value of 0 is known. 


    Now, one can carry out testing in two ways. Either a particular test can be used, or simply the mean of the distribution can be calculated using the observed values of X.


    Suppose, after calculation, the mean value comes out to be X. Two cases may arise.


    Case I: 0=X

    In this case, the observed data does not contradict the null hypothesis, so the null hypothesis is not rejected in favor of the alternate hypothesis. 


    Case II: 0X
    In this case, the observed data contradicts the null hypothesis, so it gets rejected in favor of the alternate hypothesis.

    How do we correctly calculate the p-value to make an informed decision to accept or reject our null and alternate hypothesis?

    The p-value method of hypothesis testing is used to check the significance of the null and alternate hypotheses in a testing problem. But before calculating the p-value, several steps have to be followed. 


    Generating a Test Statistic


    A testing problem is generally carried out by using the transformation method to generate a test statistic, the value of which is used to determine whether to accept or reject the null hypothesis. 


    Determining the Critical Region


    After determining the test statistic, you can calculate a critical region. The critical region can be defined as a set of limits within which the calculated value of the test statistic should lie for the null hypothesis not to be rejected. 


    The region lying between these two limits, also known as critical points, is known as the region of acceptance denoted by W. The region outside the limits is known as the rejection region, which is represented by A.


    Selection of Level of Significance


    The level of significance, denoted by , denotes the probability of rejecting a true null hypothesis. It is also used to determine the critical region of the test statistic distribution under the null hypothesis. 

    The significance level is mostly 5%, but differs from problem to problem and is usually provided to the experimenter. 


    P-value Calculation


    Consider a testing problem where the main population is denoted by X1,X2, X3, ..., XN which follows a normal distribution (independently and identically)

    Let denote the population mean and denote the standard deviation. 

    Let denote the level of significance.


    Now, from the above population of size N, a sample of size n is chosen randomly. 

    Let the random samples be denoted by  x1,x2, x3, ..., xn.

    Let x be the sample mean and s be the standard deviation. 

    So the standard error is given by:

    SE = n


    To test: H0 against H1


    Let Z denote the test statistic. 

    We define Z as:

    Z =(x-)SE


    So a calculated value of Z can be obtained using the observed values of the random sample denoted by Zobs.


    Under H0Z ~ N(0,1)

    The P-value can be calculated by:

    p = 1 - Probability (Zobs) 


    Criteria for Acceptance of H0


    Based on the P-value, the null hypothesis will be not be rejected in favor of the alternative hypothesis if 

    p > level of significance ().


    Criteria for Rejection of H0

    Based on the P-value, it can reject the null hypothesis in favor of the alternative hypothesis if  p < level of significance ().


    P-value

    In general, the P-value associated with a test statistic in a testing problem denotes the probability that a given point lies in withing the critical region. Experimenters use these values to decide whether to accept or reject a null hypothesis. 


    So, P-value or Probability value is a measure of the probability of occurrence of the event under study by the experimenter under the conditions of a null hypothesis.  


    Example:


    Let there be a bulb manufacturer who claims that a particular lot of bulbs have a lifetime of 
    units. Suppose N bulbs are present in the lot. 


    This will constitute a testing problem of the form:


    To test: H0: Average lifetime of the bulbs is units

    Against

    H1: Average lifetime of the bulbs is not units.


    Let a sample of size n be drawn randomly from the N bulb.


    Now, if on calculation the average lifetime of the n bulbs attaints a value very close to (exact value can never be attained due to underlying errors), then the value of the calculated test statistic chosen will match the value of the statistic assumed under the conditions of the null hypothesis. In this case, the P-value will be close to 1 (but never equal to 1).


    Suppose the average lifetime of the n bulbs differs significantly from, then the calculated value of the test statistic will also differ significantly from the value that the test statistic assumes under the conditions of the null hypothesis. In this case, the P-value will be close to 0 (but never equal to 0).

    Type I Error and Type II Error

    In a testing problem, the null hypothesis is not rejected in favor of the alternate hypothesis if the calculated value of the test statistic (denoted by Tcalc, say) chosen falls within the region of acceptance, denoted by W


    If the value of Tcalc falls outside W, then the null hypothesis is rejected in favor of the alternate hypothesis. 


    Type I Error


    Such a case may arise wherein Tcalc W, still the null hypothesis gets rejected. 

    This type of error is known as type I error. 


    Definition:

    The error committed by rejecting a true null hypothesis is known as a type I error. 


    Type II Error


    It may also happen that
    Tcalc W, but still, the null hypothesis does not get rejected in favor of the alternate hypothesis. This type of error is known as type II error.

    Definition:

    The error committed by accepting a false null hypothesis is known as a type II error. 


    Situation




    Decision

    H0 True

    H0 False

    H0 Rejected 

    Type I Error

    Correct Decision

    H0 Not Rejected 

    Correct Decision

    Type II Error

    In a testing problem, the choice of the null hypothesis depends highly should be made keeping in mind both types of errors. A test is termed as good if both types of errors are kept under control since, for practical purposes, it is impossible to get rid of any errors. 


    Now, it is assumed that the commission of the errors is a random event. As such, the experimenters can easily calculate the probabilities associated with them.


    Since the problem of hypothesis testing consists of a missing parameter (say ), the probabilities will also depend on it.


    Probability Associated With Type I Error


    The probability of type I error associated with is given by:

    P [Type I Error] =P [(X1,X2, X3, ..., XN) W]= P(W), 0 

    Where 

    X1,X2, X3, ..., XN denotes the population under study

    W denotes the acceptance region 

    0 denotes a specified proper subset of the parameter space


    Let be any number such that 0<<1. This value indicates the level at which the probability of type I error should be kept for a good test. So we have,

    P(W) = , 0 is known as a test's significance level. 


    Probability Associated With Type II Error


    The probability of type Ii error associated with is given by:

    P [Type II Error] =P [(X1,X2, X3, ..., XN) A]= P(A), -0 

    Where 

    X1,X2, X3, ..., XN denotes the population under study

    A denotes the rejection region 

    -0 denotes a specified proper subset of the parameter space


    Relationship Amid the Probabilities of Type I and Type II Error

    The region of acceptance, W, and the rejection region A can be thought of as two sets in the cartesian plane. The culmination of these two sets forms the entire range of values for the test. 


    Both these regions are compliments of each other, i.e., W=AC

    Where Ac is the set complimentary to A.


    So, the probability of type II error can also be written as:

    P(A) = P(WC)= 1-P(W)

    For -0


    The probability () =P(W) is a function of () is called the power function of the test. 

    We have:

    () = the probability of type I error associated with , 0

    () = 1 - the probability of type II error associated with , -0

    The power function is used to judge the nature of the whole test.

    Create a hypothesis statement

    The null and alternative hypotheses statements corresponding to a testing problem differ from problem to problem. 

    Usually, the claim made about the parameter is chosen as the alternative hypothesis when dealing with a problem. Consider the following problem:


    Problem:

    A lightbulb manufacturer packs their bulbs into cartons, each carton containing 100 bulbs. Out of these 100 bulbs, 30 bulbs are picked at random testing. According to the manufacturer, the average lifetime of a bulb is 1,000 hours. Now, a new manufacturing process has been introduced, which is said to increase the average lifetime of the bulbs. Check whether the new approach is effective, assuming that the lifetime of the bulbs follows a normal distribution. 


    Solution:

    In the above problem, it has been provided that the average lifetime of the bulbs using the old method is 1,000 hours. 

    A claim has been made that the new manufacturing process will increase the lifetime of the bulb, i.e., it will be more than 1,000 hours. 


    So, we have to test if the new process actually increases the lifetime of the bulbs.


    Let denote the lifetime of the bulbs. 

    As such the testing problem can be written as:


    To test: H0 : =1,000 against H1 : >1,000

    Decide the significance level

    The level of significance of a test () is the probability of type I error. This is usually provided to the experimenter.

    Calculate the test statistic

    A test statistic is used to decide the rejection criteria for the null hypothesis in a testing problem. Different tests have different test statistics

    Test Statistic for the Mean of a Normal Distribution


    Let  X1,X2, X3, ..., Xn denote a set of random samples that follow a normal distribution independently and identically with mean and variance 2. Here both the mean and variance are unknown parameters. 


    Let the testing problem be defined as


    To test: H0 : =0 against H1 : = 1


    Where 10 


    We define the test statistic as -


    T = (X-)SE


    Where X is the mean of the population from which the random sample has been sampled


    And SE is the standard error


    Now, under H0,


    T =(X-0)SE ~ tn-1


    So the value of the test statistic can be calculated at a particular level of significance from a t-distribution table 


    The retrieved value of the test statistic can be computed methodically by using the observations.


    Test Statistic for the Variance of a Normal Distribution


    Let  X1,X2, X3, ..., Xn denote a set of random samples that follow a normal distribution independently and identically with mean and variance 2. Here both the mean and variance are unknown parameters.


    Let the testing problem be defined as


    To test:
    H0 : 2=02 against H1 :2=12


    Where 1202 


    We define the test statistic as 


    T=
    (n-1)s22


    Where s2 denotes the sample variance


    Under H0,


    T ~ n-12


    So the value of the test statistic can be calculated at a particular level of significance from a chi-square distribution table. 


    The observed value of the test statistic is computed methodically by using the observations.

    Comparing test statistic to the critical value

    After calculating the value of the test statistic T, denoted by Tobs (say) we need to compare it to the critical value to determine whether H0 gets rejected. 


    The test statistic’s critical value is obtained from tables provided or by using the software. The critical value is calculated at a particular level of significance ,say. 


    Suppose the calculated value of the test statistic comes out to be greater than the critical value at significance level. In such a case, the null hypothesis is rejected in favor of the alternate hypothesis.

    Report your findings

    Correctly reporting the results of an experiment is one of the most crucial tasks of the experimenter. While dealing with the problem of hypothesis testing, a particular syntax is followed by statisticians all around the globe. 


    After comparing the value of the test statistic to the critical value, either the null hypothesis will get rejected, or it will not get rejected. 


    Case 1: Null Hypothesis Rejected


    As the calculated value of the test statistic is greater than the critical value, we reject H0 in favor of H1.


    Case 1: Null Hypothesis Is Not Rejected


    As the calculated value of the test statistic is less than the critical value, we do not reject H0 in favor of H1.

    It is also preferable to report all the values obtained in a tabular format.

    One sample t-test

    One sample t-test is generally used to determine if a significant difference exists between the means of an unknown population and a particular value. It is used when the standard deviation of the population is unknown. 


    Assumptions:

    1. Data must be continuous

    2. The data must follow a normal distribution 

    3. Sampling should be done using simple random sample techniques such that the probability of selection of each sample is equal


    The pre-requisites for performing this test are the population mean, sample size, sample mean, sample standard deviation, and sample size. 


    Let  X1,X2, X3, ..., Xn denote a set of random samples that follow a normal distribution independently and identically with mean and variance 2, where the variance is unknown.


    Let the testing problem be denoted as:


    To test: H0 : =0 against H1 : 0 (two-tailed test)

                  H0 : =0 against H1 : > 0 (right-tailed test)

                  H0 : =0 against H1 : < 0 (left-tailed test)

    Where is the value of the hypothesized mean


    Now, the standard error of the sample is given by:

    SE = sn

    Where s is the standard deviation of the random sample


    The test statistic is defined as 

     T = (X-)SE =n(X-)s 


    Under H0,

     T = (X-0)SE =n(X-0)s ~ tn-1

    I.e., the test statistic follows a t-distribution with degrees of freedom n-1


    The critical value if given by: Tctitcal= t; n-1 (for a one tailed test)

                                                                     t2; n-1 (for a two tailed test)

    Where is the level of significance

    One sample z-test

    In a testing problem, z-test is used to check the significant difference between two population means when the standard deviation of the population is known. 


    Assumptions:

    1. Data should be continuous

    2. The data should follow a normal distribution

    3. The sample should be generated from the population using simple random sampling techniques, such that the probabilities of selecting the samples are equal. 

    4. The population standard deviation should be known. 


    Let  X1,X2, X3, ..., Xn denote a set of random samples that follow a normal distribution independently and identically with mean and variance 2, where the variance is known.


    Let the testing problem be denoted as:


    To test: H0 : =0 against H1 : 0 (two-tailed test)

                  H0 : =0 against H1 : > 0 (right-tailed test)

                  H0 : =0 against H1 : < 0 (left-tailed test)

    Where is the value of the hypothesized mean


    The test statistic is defined as

    Z=X-/n

    Where X=i=1nXin


    Under H0,

     Z = (X-0)/n  ~ N(0,1)

    I.e, the test statistic follows a standard normal distribution


    The critical value is given by: Zctitcal= z; n-1 (for a one-tailed test)

                                                                                  z2; n-1 (for a two-tailed test)

    Where is the level of significance

    Two independent samples t-test

    The use of t-test can be extended beyond one sample, i.e., it can also be used to check for a significant difference between the means of two different independent populations. 


    Assumptions:

    1. Data must be continuous

    2. Random sampling techniques from the population should generate the data.

    3. The data should follow a normal distribution

    4. The variances of the two independent groups should be equal


    Let X1,X2, X3, ..., XnX denote the first random sample and Y1,Y2, Y3, ..., YnY denote the second random sample such that they are independent of each other. 


    Let the first sample follow a normal distribution with mean X and variance sX2.

    Let the second sample follow a normal distribution with mean Y and variance sY2.

    To test: H0 : X=Y against H1 : XY (two-tailed test)

                  H0 : X=Y against H1 : X> Y (right-tailed test)

                  H0 : X=Y against H1 : X< Y (left-tailed test)


    We define the test statistic as

    T=X-YSE(1nX+1nY)

    Where SE is the pooled standard deviation is given by

    SE ={(nx-1)sX2}+{nY-1)sY2}nX+nY-2


    Under H0, T ~ tnX+nY-2

    The critical value is given by: Tctitcal=t; nX+nY-2 (for a one-tailed test)

                                                                     t2; nX+nY-2 (for a two-tailed test )

    Where is the level of significance


    Paired t-test

    A paired t-test is used to check for the presence of any significant difference between two variables under the same subject. Usually, the two variables are separated by time.


    Example:

    An experimenter may want to find if there is any significant difference between deaths due to COVID-19 in May 2020 as compared to June 2020.


    So, a paired t-test is used to check whether the mean difference between the pairs of observations differs significantly.


    Assumptions:

    1. The samples under study must be independent, i.e., any measurements made on the first sample should not affect the second sample. 

    2. Each sample pair must be obtained from the same subject, e,g., the weights of patients before and after undergoing a diet.

    3. Each sample pair must follow a normal distribution.


    Let X1,X2, X3, ..., Xn denote the first random sample and Y1,Y2, Y3, ..., Yn denote the second random sample such that they are independent of each other. Let both of them be normally distributed.


    Let Z be a new random variable denoting the difference between the two samples, i.e.,

    Z=X-Y


    Let Z denote the mean of the differences and sZ2 denote the variance of the difference.

    To test: H0 : Z=0 against H1 : Z0 (two-tailed test)

                  H0 : Z=0 against H1 : Z>0 (right-tailed test)

                  H0 : Z=0 against H1 : Z<0 (left-tailed test)


    The test statistic is given by

    T=ZsZ/n


    Under H0, T ~ tn-1


    The critical value if given by: Tctitcal= t; n-1 (for a one tailed test)

                                                                     t2; n-1 (for a two tailed test)

    Where is the level of significance


    ANOVA and post hoc analysis

    If observations are taken from a population with a given mean, it is not necessary that they will be identical. Due to the presence of random observation error, the observations fluctuate around the mean. This is a natural, inevitable variation. On top of this, another source of variation or sources of variation is deliberately introduced or suspected to enter due to circumstances beyond our control. 

    Hence, observations are heterogeneous or not homogeneous concerning the source or sources of variation. 


    Example:


    An experimenter wishes to assess the effect of a sleeping drug on the average amount of sleep of patients.


    A deliberately introduced source of variation, for example, a sleeping drug, is called “treatment” or “factor”. Thus certain patients who do not receive the “treatment” form one group, and the other groups are formed by changing the “dose” of the drug. Besides the drug, the patients can be classified according to other factors such as age or gender.


    The effect of these sources of variation; that is, treatment can be assessed by analyzing the total variation and spilling it into components corresponding to these sources of variation.

    Now, this analysis can be done in several ways, Analysis of Variance or ANOVA being one such method. The analysis of variance is a body of statistical methods of analyzing observations assumed to be of the structure


    Yi= b1xi1+b2xi2+...+bpxip+ei , i=1(1)n j=1(1)p


    , where the coefficients {xij} are the values of “counter variables” or “indicator variables’ which refer to the presence or absence of the effects {bj} in the conditions under which the observations are taken as: xij is the number of times bj occurs in the ith observation and this is usually 0 or 1. In general, in the analysis of variance, all factors are treated qualitatively.


    Now the experimenter may also be interested to know if the effect of any of the treatments in an ANOVA setup differs significantly concerning the other treatments.


    Let the data be modeled as

    Yi=+i+ei , i=1(1)n

    Where is the process mean

    i denotes the effect due to the ith treatment

    ei is the random error associated with the process


    To test: H0: 1=2=3= ... = n=0 against H1: not H0

    Now there may be two cases that the experimenter may face.


    Case I: Null Hypothesis Is Not Rejected

    In this case, since H0 is not rejected in favor of H1, no significant difference exists between the effect of the treatments. 


    Case II: Null Hypothesis Rejected

    If the null hypothesis gets rejected in favor of the alternate hypothesis, then the experimenter can claim that the effects due to one or more treatments are different. 


    Pairwise testing is used on all treatment pairs to determine which treatments are responsible for the difference. This process is known as post hoc analysis.

    Why an online Hypothesis Testing Course is better than Offline Hypothesis Testing Course

    Many courses are available today that provide quality education on hypothesis testing. These courses are especially beneficial because they will save you a lot of time and energy. 


    The main advantage of opting for an online course is that you can learn at your own pace. In offline courses, once a topic is covered, it will be up to you to learn it because the professor may move on to the next topic without waiting for you to finish. This does not happen in online courses. Online courses follow your pace of learning and thus offer better learning opportunities. 


    Another significant advantage of online courses is that you can attend classes from the comfort of your home, significantly reducing travel expenses. 


    When you opt for online courses, you will be provided with a choice of instructors and can select someone who suits your needs best. This will allow you to learn much more effectively than offline courses, where your choices remain limited. 


    Online courses also have excellent doubt-clearing facilities that offline courses lack. 


    So, in light of the given data, an online hypothesis testing course is better than an offline one.

    Hypothesis Testing Course Syllabus

    The syllabus for a hypothesis testing course covers:


    1. Test of a statistical hypothesis and critical region

    2. Type I and type II errors

    3. Level of significance and power of test

    4. Optimum tests in different situations

    5. Unbiased tests

    6. Neyman-Pearson lemma

    7. Construction of most powerful (MP) and uniformly most powerful (UMP) critical regions

    8. MP and UMP regions in random sampling from a normal distribution

    9. Construction of type A regions

    10. Construction of type A1 regions

    11. Optimum regions and sufficient statistics

    12. Randomized tests

    13. Composite hypotheses and similar regions

    14. Similar regions and complete sufficient statistics

    15. Construction of most powerful similar regions

    16. Test to derive the mean of a normal distribution

    17. Test for the variance of a normal distribution

    18. Monotonicity of power function

    19. Consistency

    20. Invariance

    21. Likelyhood-ratio tests

    22. Comparing the means of k normal distributions with common variance

    23. Properties of likelihood-ratio tests

    Projecting Hypothesis Testing Industry Growth in 2022-23

    The complex process of Hypothesis testing is being broadly leveraged industry-wide to make well-informed, data-driven decisions towards assured results. The power of Hypothesis testing enables professionals to test their theories before putting them into action, which can significantly benefit organisations to reap value while cutting risks of potential repercussions. 


    Its active implementation in business, as well as investment opportunities, is helping experts perform statistical analysis against containing datasets and receive decisive predictions towards a winning strategy. As Hypothetical testing is strengthening its statistical methods to enhance accuracy, more and more businesses are incorporating it to test their theories before committing resources to it, leading to a thriving future projection in the coming days. 

    The Accelerating Demand for the Hypothesis Testing Courses in India

    Today, all major jobs are in the data science field. A data science course may just land you your dream job. 


    Hypothesis testing is one of the most pivotal concepts in statistics. This concept is used in all industries. As a result, there has been a huge demand for hypothesis testing courses in India. 


    These courses offer all the knowledge that any data scientist may possess, allowing you to apply for your dream job no matter your educational background.

    Hypothesis Testing Specialist Salary In India

    Hypothesis testing is a part of statistics. So, solving these problems generally falls on the data scientists or data analysts who deal with statistics as a whole.


    The median salary of data scientists in India is Rs. 46,953 per annum. 


    The entry-level salary for an analyst with an experience of less than a year is Rs. 3,67,000. For an experienced data analyst with more than 20 years of experience, the salary is Rs. 2 million.

    Factors on which Hypothesis Testing Specialist salary in India depends

    Different factors affect the job of a data analyst. A base-level data analyst should know basic statistics and software like python, SQL, and R. Apart from these, they must also possess project management and organizational skills. 


    Data analysts should also have an analytical mind that allows them to work seamlessly with large unstructured data sets. 


    Other factors that determine their salary are the company they work at, its size and reputation, their position, work experience, and geographic location.

    Hypothesis Testing Specialist Salary Abroad

    The median salary of a data analyst in the US is $ 63,259 (Rs. 49,43,545.35) per annum. 


    The median salary of a data analyst in the UK is £ 28,218 (Rs. 2706930.73) per annum

    View More

    Why upGrad?

    1000+ Top companies

    1000+

    Top Companies

    Salary Average Hike

    50%

    Average Salary Hike

    Global Universities

    Top 1%

    Global Universities

    Schedule 1:1 Counseling with upGrad

    Talk to a Career Expert

    Data Science Courses (11)

    Instructors

    Learn from India’s leading Data Science faculty & industry experts

    Our Learners Work At

    Top companies from all around the world have recruited upGrad alumni

    Data Science Free Courses

    Data Science

    Data Science

    Courses to get started with your Data Science and ML Career

    20 Free Courses

    Data Science Videos

    Data Science Blogs

    Other Domains

    The upGrad Advantage

    Strong hand-holding with dedicated support to help you master Data Science
    benefits

    Learning Support

    Learning Support
    Industry Expert Guidance
    • - Interactive Live Sessions with leading industry experts covering curriculum + advanced topics
    • - Personalised Industry Session in small groups (of 10-12) with industry experts to augment program curriculum with customized industry based learning
    Student Support
    • - Student Support is available 7 days a week, 24*7
    • - For urgent queries, use the Call Back option on the platform.
    benefits

    Career Assistance

    Career Assistance
    Career Mentorship Sessions (1:1)
    • Get mentored by an experienced industry expert and receive personalised feedback to achieve your desired outcome
    High Performance Coaching (1:1)
    • Get a dedicated career coach after the program to help track your career goals, coach you on your profile, and support you during your career transition journey
    AI Powered Profile Builder
    • Obtain specific, AI powered inputs on your resume and Linkedin structure along with content on real time basis
    Interview Preparation
    • - Get access to Industry Experts and discuss any queries before your interview
    • - Career bootcamps to refresh your technical concepts and improve your soft skills
    benefits

    Practical Learning and Networking

    Practical Learning and Networking
    Networking & Learning Experience
    • - Live Discussion forum for peer to peer doubt resolution monitored by technical experts
    • - Peer to peer networking opportunities with a alumni pool of 10000+
    • - Lab walkthroughs of industry-driven projects
    • - Weekly real-time doubt clearing sessions
    benefits

    Job Opportunities

    Job Opportunities
    upGrad Opportunities
    • - upGrad Elevate: Virtual hiring drive giving you the opportunity to interview with upGrad's 300+ hiring partners
    • - Job Opportunities Portal: Gain exclusive access to upGrad's Job Opportunities portal which has 100+ openings from upGrad's hiring partners at any given time
    • - Be the first to know vacancies to gain an edge in the application process
    • - Connect with companies that are the best match for you

    Did not find what you are looking for? Get in touch with us now!

    Continue with email

    Let’s Get Started

    Let’s Get Started

    Data Science Course Fees

    Programs

    Fees

    Master of Science in Data Science from LJMU

    INR 4,99,000*

    Executive Post Graduate Programme in Data Science from IIITB

    INR 2,99,000*

    Master of Science in Data Science from UOA

    INR 7,50,000*

    Professional Certificate Program in Data Science for Business Decision Making from IIMK

    INR 1,50,000*

    Advanced Certificate Programme in Data Science

    INR 99,000*

    Industry Projects

    Learn through real-life industry projects sponsored by top companies across industries
    • Collaborative projects with peers
    • In-person learning with expert mentors
    • Personalised feedback to facilitate improvement

    Frequently Asked Questions about Hypothesis Testing Course

    What is the use of hypothesis testing in real life?

    Real-life hypothesis testing allows researchers to test new theories before implementing them. It is used in different industries to set standards for their products. It is especially helpful to statisticians when designing an experiment with many parameters. 

    What is the difference between simple and composite hypotheses?

    Statistical hypotheses are of two types. Simple and composite. 

     

    A statistical hypothesis that specifies the distribution of the parent population from which the random samples to be used for testing has been generated is known as a simple hypothesis. 

     

    A statistical hypothesis that does not specify the distribution of the parent population from which the random samples to be used for testing has been generated is known as a composite hypothesis. 

    What statistical concepts are needed to get a good grasp on hypothesis testing?

    One needs to know probability theory, the different types of probability distributions, and statical inference to get a good grasp on the testing of a hypothesis.