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Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid.
A null hypothesis and an alternative hypothesis are set up before performing the hypothesis testing. This helps to arrive at a conclusion regarding the sample obtained from the population. In this article, we will learn more about hypothesis testing, its types, steps to perform the testing, and associated examples.
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Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution . It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.
Hypothesis testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypotheses will always be mutually exclusive. This means that if the null hypothesis is true then the alternative hypothesis is false and vice versa. An example of hypothesis testing is setting up a test to check if a new medicine works on a disease in a more efficient manner.
The null hypothesis is a concise mathematical statement that is used to indicate that there is no difference between two possibilities. In other words, there is no difference between certain characteristics of data. This hypothesis assumes that the outcomes of an experiment are based on chance alone. It is denoted as \(H_{0}\). Hypothesis testing is used to conclude if the null hypothesis can be rejected or not. Suppose an experiment is conducted to check if girls are shorter than boys at the age of 5. The null hypothesis will say that they are the same height.
The alternative hypothesis is an alternative to the null hypothesis. It is used to show that the observations of an experiment are due to some real effect. It indicates that there is a statistical significance between two possible outcomes and can be denoted as \(H_{1}\) or \(H_{a}\). For the above-mentioned example, the alternative hypothesis would be that girls are shorter than boys at the age of 5.
In hypothesis testing, the p value is used to indicate whether the results obtained after conducting a test are statistically significant or not. It also indicates the probability of making an error in rejecting or not rejecting the null hypothesis.This value is always a number between 0 and 1. The p value is compared to an alpha level, \(\alpha\) or significance level. The alpha level can be defined as the acceptable risk of incorrectly rejecting the null hypothesis. The alpha level is usually chosen between 1% to 5%.
All sets of values that lead to rejecting the null hypothesis lie in the critical region. Furthermore, the value that separates the critical region from the non-critical region is known as the critical value.
Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below:
We will learn more about these test statistics in the upcoming section.
Selecting the correct test for performing hypothesis testing can be confusing. These tests are used to determine a test statistic on the basis of which the null hypothesis can either be rejected or not rejected. Some of the important tests used for hypothesis testing are given below.
A z test is a way of hypothesis testing that is used for a large sample size (n ≥ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known. It can also be used to compare the mean of two samples. It is used to compute the z test statistic. The formulas are given as follows:
The t test is another method of hypothesis testing that is used for a small sample size (n < 30). It is also used to compare the sample mean and population mean. However, the population standard deviation is not known. Instead, the sample standard deviation is known. The mean of two samples can also be compared using the t test.
The Chi square test is a hypothesis testing method that is used to check whether the variables in a population are independent or not. It is used when the test statistic is chi-squared distributed.
One tailed hypothesis testing is done when the rejection region is only in one direction. It can also be known as directional hypothesis testing because the effects can be tested in one direction only. This type of testing is further classified into the right tailed test and left tailed test.
Right Tailed Hypothesis Testing
The right tail test is also known as the upper tail test. This test is used to check whether the population parameter is greater than some value. The null and alternative hypotheses for this test are given as follows:
\(H_{0}\): The population parameter is ≤ some value
\(H_{1}\): The population parameter is > some value.
If the test statistic has a greater value than the critical value then the null hypothesis is rejected
Left Tailed Hypothesis Testing
The left tail test is also known as the lower tail test. It is used to check whether the population parameter is less than some value. The hypotheses for this hypothesis testing can be written as follows:
\(H_{0}\): The population parameter is ≥ some value
\(H_{1}\): The population parameter is < some value.
The null hypothesis is rejected if the test statistic has a value lesser than the critical value.
In this hypothesis testing method, the critical region lies on both sides of the sampling distribution. It is also known as a non - directional hypothesis testing method. The two-tailed test is used when it needs to be determined if the population parameter is assumed to be different than some value. The hypotheses can be set up as follows:
\(H_{0}\): the population parameter = some value
\(H_{1}\): the population parameter ≠ some value
The null hypothesis is rejected if the test statistic has a value that is not equal to the critical value.
Hypothesis testing can be easily performed in five simple steps. The most important step is to correctly set up the hypotheses and identify the right method for hypothesis testing. The basic steps to perform hypothesis testing are as follows:
The best way to solve a problem on hypothesis testing is by applying the 5 steps mentioned in the previous section. Suppose a researcher claims that the mean average weight of men is greater than 100kgs with a standard deviation of 15kgs. 30 men are chosen with an average weight of 112.5 Kgs. Using hypothesis testing, check if there is enough evidence to support the researcher's claim. The confidence interval is given as 95%.
Step 1: This is an example of a right-tailed test. Set up the null hypothesis as \(H_{0}\): \(\mu\) = 100.
Step 2: The alternative hypothesis is given by \(H_{1}\): \(\mu\) > 100.
Step 3: As this is a one-tailed test, \(\alpha\) = 100% - 95% = 5%. This can be used to determine the critical value.
1 - \(\alpha\) = 1 - 0.05 = 0.95
0.95 gives the required area under the curve. Now using a normal distribution table, the area 0.95 is at z = 1.645. A similar process can be followed for a t-test. The only additional requirement is to calculate the degrees of freedom given by n - 1.
Step 4: Calculate the z test statistic. This is because the sample size is 30. Furthermore, the sample and population means are known along with the standard deviation.
z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
\(\mu\) = 100, \(\overline{x}\) = 112.5, n = 30, \(\sigma\) = 15
z = \(\frac{112.5-100}{\frac{15}{\sqrt{30}}}\) = 4.56
Step 5: Conclusion. As 4.56 > 1.645 thus, the null hypothesis can be rejected.
Confidence intervals form an important part of hypothesis testing. This is because the alpha level can be determined from a given confidence interval. Suppose a confidence interval is given as 95%. Subtract the confidence interval from 100%. This gives 100 - 95 = 5% or 0.05. This is the alpha value of a one-tailed hypothesis testing. To obtain the alpha value for a two-tailed hypothesis testing, divide this value by 2. This gives 0.05 / 2 = 0.025.
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Important Notes on Hypothesis Testing
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What is hypothesis testing.
Hypothesis testing in statistics is a tool that is used to make inferences about the population data. It is also used to check if the results of an experiment are valid.
The z test in hypothesis testing is used to find the z test statistic for normally distributed data . The z test is used when the standard deviation of the population is known and the sample size is greater than or equal to 30.
The t test in hypothesis testing is used when the data follows a student t distribution . It is used when the sample size is less than 30 and standard deviation of the population is not known.
The formula for a one sample z test in hypothesis testing is z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) and for two samples is z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).
The p value helps to determine if the test results are statistically significant or not. In hypothesis testing, the null hypothesis can either be rejected or not rejected based on the comparison between the p value and the alpha level.
When the rejection region is only on one side of the distribution curve then it is known as one tail hypothesis testing. The right tail test and the left tail test are two types of directional hypothesis testing.
To get the alpha level in a two tail hypothesis testing divide \(\alpha\) by 2. This is done as there are two rejection regions in the curve.
The science of statistics deals with the collection, analysis, interpretation, and presentation of data . We see and use data in our everyday lives.
In your classroom, try this exercise. Have class members write down the average time—in hours, to the nearest half-hour—they sleep per night. Your instructor will record the data. Then create a simple graph, called a dot plot, of the data. A dot plot consists of a number line and dots, or points, positioned above the number line. For example, consider the following data:
5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9.
The dot plot for this data would be as follows:
Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?
Where do your data appear to cluster? How might you interpret the clustering?
The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics.
In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics . Two ways to summarize data are by graphing and by using numbers, for example, finding an average. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from good data. The formal methods are called inferential statistics . Statistical inference uses probability to determine how confident we can be that our conclusions are correct.
Effective interpretation of data, or inference, is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.
Statistics, like all other branches of mathematics, uses mathematical models to describe phenomena that occur in the real world. Some mathematical models are deterministic. These models can be used when one value is precisely determined from another value. Examples of deterministic models are the quadratic equations that describe the acceleration of a car from rest or the differential equations that describe the transfer of heat from a stove to a pot. These models are quite accurate and can be used to answer questions and make predictions with a high degree of precision. Space agencies, for example, use deterministic models to predict the exact amount of thrust that a rocket needs to break away from Earth’s gravity and achieve orbit.
However, life is not always precise. While scientists can predict to the minute the time that the sun will rise, they cannot say precisely where a hurricane will make landfall. Statistical models can be used to predict life’s more uncertain situations. These special forms of mathematical models or functions are based on the idea that one value affects another value. Some statistical models are mathematical functions that are more precise—one set of values can predict or determine another set of values. Or some statistical models are mathematical functions in which a set of values do not precisely determine other values. Statistical models are very useful because they can describe the probability or likelihood of an event occurring and provide alternative outcomes if the event does not occur. For example, weather forecasts are examples of statistical models. Meteorologists cannot predict tomorrow’s weather with certainty. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.
Probability is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is 1 2 1 2 or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction 996 2,000 996 2,000 is equal to .498 which is very close to .5, the expected probability.
The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client's investments.
In statistics, we generally want to study a population . You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample . The idea of sampling is to select a portion, or subset, of the larger population and study that portion—the sample—to gain information about the population. Data are the result of sampling from a population.
Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16-ounce can contains 16 ounces of carbonated drink.
From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class as a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Since we do not have the data for all math classes, that statistic is our best estimate of the average for the entire population of math classes. If we happen to have data for all math classes, we can find the population parameter. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.
One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. In order to have an accurate sample, it must contain the characteristics of the population in order to be a representative sample . We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.
A variable , usually notated by capital letters such as X and Y , is a characteristic or measurement that can be determined for each member of a population. Variables may describe values like weight in pounds or favorite subject in school. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X —calculate the average number of points earned, for example—but it makes no sense to do math with values of Y —calculating an average party affiliation makes no sense.
Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.
Two words that come up often in statistics are mean and proportion . If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three. Your mean score would be 84.3 to one decimal place. If, in your math class, there are 40 students and 22 are males and 18 females, then the proportion of men students is 22 40 22 40 and the proportion of women students is 18 40 18 40 . Mean and proportion are discussed in more detail in later chapters.
The words mean and average are often used interchangeably. In this book, we use the term arithmetic mean for mean.
Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.
We want to know the mean amount of extracurricular activities in which high school students participate. We randomly surveyed 100 high school students. Three of those students were in 2, 5, and 7 extracurricular activities, respectively.
The population is all high school students.
The sample is the 100 high school students interviewed.
The parameter is the mean amount of extracurricular activities in which all high school students participate.
The statistic is the mean amount of extracurricular activities in which the sample of high school students participate.
The variable could be the amount of extracurricular activities by one high school student. Let X = the amount of extracurricular activities by one high school student.
The data are the number of extracurricular activities in which the high school students participate. Examples of the data are 2, 5, 7.
Find an article online or in a newspaper or magazine that refers to a statistical study or poll. Identify what each of the key terms—population, sample, parameter, statistic, variable, and data—refers to in the study mentioned in the article. Does the article use the key terms correctly?
Determine what the key terms refer to in the following study.
A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.
1. Population ____ 2. Statistic ____ 3. Parameter ____ 4. Sample ____ 5. Variable ____ 6. Data ____
1. f ; 2. g ; 3. e ; 4. d ; 5. b ; 6. c
As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies (The Data and Story Library, n.d.). Here is the criterion they used.
Speed at which Cars Crashed | Location of (i.e., dummies) |
35 miles/hour | Front seat |
Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.
The population is all cars containing dummies in the front seat.
The sample is the 75 cars, selected by a simple random sample.
The parameter is the proportion of driver dummies—if they had been real people—who would have suffered head injuries in the population.
The statistic is proportion of driver dummies—if they had been real people—who would have suffered head injuries in the sample.
The variable X = whether driver dummies—if they had been real people—would have suffered head injuries.
The data are either: yes, had head injury, or no, did not.
An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.
The population is all medical doctors listed in the professional directory.
The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population.
The sample is the 500 doctors selected at random from the professional directory.
The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the sample.
The variable X records whether a doctor has or has not been involved in a malpractice suit.
The data are either: yes, was involved in one or more malpractice lawsuits; or no, was not.
Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average—mean—number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.
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Is this result even possible.
Omar Elgabry
OmarElgabry's Blog
This series of articles inspired by Statistics with R Specialization from Duke University . The full series of articles can be found here .
Have you ever came upon situations, outcomes, or events that just seem odd?
In a city made up of 51% women, where jury pools are said to be chosen at random, a certain jury pool of 50 people contains only 8 women.
When you hear things like this, they make you think. It doesn’t seem right. Is that even possible?.
And if it is possible, how likely is it that it could have happened at random?. Sometimes these questions and the related answers may help us make decisions.
Perhaps you work at a healthcare company. Your company has developed a drug to treat the common cold. When testing this new medicine on a random sample of 250 people with the common cold, it’s found that these patients recovered about 1.2 days sooner that those that did not take this drug.
Is this significant? Could this sample just be the result of chance, or did this drug have an impact?.
This is where hypothesis testing comes in.
Statistical Inference is the process of drawing conclusions about the population from data.
(~) Bank managers were randomly given 48 resume of employees for promotion. Half of resumes are male, and half is female. The percentage of males promoted were 21 out of 24 (88%). The percentage of females promoted were 14 out of 24 (58%). The difference is 30%. Does the data provide a convincing evidence that there is a discrimination between male and female?
In general …
Null hypothesis : There is nothing going on. The promotion and gender are independent. There is no gender discrimination. And, the observed difference in proportions is simply due to chance.
Alternative hypothesis : There is indeed something going on. The promotion and gender are dependent, there is gender discrimination. And, the observed difference in proportions, is not due to chance.
We conduct a hypothesis test under the assumption that the null hypothesis is true.
Either via simulation, or using theoretical methods that rely on the central limit theorem. We’ll discuss both methods, mainly CLT, and simulation at the end.
If the test results suggest that the data do not provide convincing evidence for the alternative hypothesis, we stick with the null hypothesis.
Otherwise, we reject the null hypothesis in favor of the alternative.
There are 5 steps to conduct a hypothesis test.
(~) A sample of 50 students was collected to measure the average number of relationships students have been in. Given that the sample average = 3.2, and standard deviation = 1.74, and standard error = 0.246. Do these data support the hypothesis that students on average have > 3 relationships?. Use 95% confidence interval.
There are two claims (hypothesis).
In the null hypothesis, usually we call it H0, we set the parameter of interest (i.e. mean) equal to (=) some value.
2. Alternative (what we want to test):
In the alternative hypothesis, usually we call it HA, often represented by a range of possible parameter values, either <, >, or != the null hypothesis value (that’s why we set H0 equal to 3).
The hypothesis are always about the population parameters and never about the sample statistics. We already know the sample statistics, we don’t need to hypothesize about them.
Get a sample and calculate the point estimate (i.e. mean) from it.
In this case, it’s the average number of relationships, which equals to 3.2
As mentioned before, one of the ways to run hypothesis test is to use theoretical methods that rely on the central limit theorem.
And so, make sure all the conditions (independence & skewness) still hold.
Hypothesis testing takes the concepts we introduced in CLT and CI, and use them when plotting the distribution.
Since we assume that the null hypothesis is true, so the distribution is normal, and centered around the null value (population mean).
With 95% CI, the white area under the curve is where most of the data lie. While the red area represent the outliers, that’s something is wrong.
And so, if the probability of the observed average of relationships is in the red area (%5 or less), then, we would say, the the observed data is statistically significant.
The p-value , is the probability of observed (or extreme) value, given the null hypothesis is true.
The extreme (unusual) value here means a value greater than the observed one.
How to calculate the p-value?
But, what does it mean?.
Under the assumption of null hypothesis, there is a 20.9% chance that a random sample of 50 students would yield sample mean of 3.2 or higher.
Since our p-value is high, or in other words, higher than 5%, we fail to reject the null hypothesis.
These data do not provide convincing evidence that students have in more than 3 relationships on average. And the difference between the null value of 3 relationships and the observed sample mean of 3.2 relationships, is simply due to chance or variability.
Instead of looking for a divergence from the null hypothesis in a specific direction (greater or less than), we might need to look in divergence in any direction.
When to choose two-sided Vs one-sided? Based on the alternative hypotheses. One-sided if its greater or less than, and two-sided if not equal.
In case of two-sided, the extreme value in p-value includes both directions.
The p-value is the probability of observed (or extreme) value …
(~) A sample of 36 of Mother’s IQ is collected with average 118.2, and sd = 6.5.
(~) A sample of 36 of Mother’s IQ is collected with average 118.2, and sd = 6.5. Perform a hypothesis test to evaluate if the observed difference between Mother’s IQ and population IQ mean is true. The population IQ mean = 100. Use alpha = 0.01.
Given its a two-sided hypothesis, the p-value = P(sample mean ≥ 118.2 OR sample mean ≤-118.2 | H0: population mean = 100) ~= 0
It means the probability of obtaining a random sample of 36 of Mothers who have IQ 118.2 or extreme on average, if in fact Mother’s IQ is truly 100 on average (null hypothesis), is almost 0.
Since p-value < alpha (1%), we have a very strong evidence against H0 .
So, we reject it, and conclude that the sample data provided shows an evidence of a difference between the average IQ score and the average IQ score for the population at large.
Would you expect a confidence interval to contain the null value (100)?.
We rejected the null, so value=100 shouldn’t be in the interval.
Whats the relationship between significance and confidence level?
In a two sided test. If we have a curve as below, where confidence level is 95%. This means the significance level is best at 5%. Why? p-value is within the 2.5% on right OR left.
In a one sided test. If the significance level is 5%, what should be the confidence level?. This means the confidence level is best at 90%. Why? p-value can only be within the 5% on right.
When using both in doing inference, make sure for both methods to agree with each other. Why? Because because anything above (or below) the confidence interval is considered “extreme value”.
To summarize:
We can make wrong decision in statistical hypothesis tests. There are two types of errors: Error 1 and 2.
Though, we have the tools necessary to know the likelihood of making these errors. The likelihood of these errors are inversely proportional. So it’s not easy to keep both those error rates down.
If alpha = 5%. This means there is about a 5% chance of making a type 1 error. This is why we prefer small values of alpha to avoid Type 1 Error.
If type one error is more dangerous or costly, we might choose a small value (even smaller than 5% ~=1%), the goal here is to be cautious about rejecting the null hypothesis, and so we demand very strong evidence favoring the alternative.
If the type two error is more dangerous or costly, we might choose a higher value (~= 10%). Increasing our alpha will have the effect of decreasing our type two 2 error. The goal here is to be cautious about failing to reject the null hypothesis when the null is actually false.
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In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.
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This probability is known as the p-value and it is used to evaluate statistical significance. p-value Given that the null hypothesis is true, the probability of obtaining a sample statistic as extreme or more extreme than the one in the observed sample, in the direction of the alternative hypothesis
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
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A simple introduction to the concept of hypothesis testing, one of the most important concepts in all of statistics.
A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a ...
Hypothesis testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of a population. A hypothesis is a claim or statement about a characteristic of a population of interest to us. A hypothesis test is a way for us to use our sample statistics to test a specific claim.
Determine the hypothesis: What are we trying to figure out? This is formally written as the null and alternative hypotheses. Calculate the evidence: This will be a test statistics and either a critical value or a p-value. Make a decision: The options will be Reject the Null Hypothesis or Do not Reject the Null Hypothesis.
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Statistics - Hypothesis Testing, Sampling, Analysis: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution.
A hypothesis, in statistics, is a statement about a population parameter, where this statement typically is represented by some specific numerical value. In testing a hypothesis, we use a method where we gather data in an effort to gather evidence about the hypothesis.
Learn about the concept and methods of statistical hypothesis testing from various ScienceDirect topics and related research articles.
Get the full course at: http://www.MathTutorDVD.comThe student will learn the big picture of what a hypothesis test is in statistics. We will discuss terms ...
Explore hypothesis testing, a fundamental method in data analysis. Understand how to use it to draw accurate conclusions and make informed decisions.
What is Hypothesis Testing in Statistics? Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution. It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.
The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives....
In this article, we are going to learn about Hypothesis Testing. It is a very important and elegant concept in Probability and Statistics.
Hypothesis testing refers to the process of choosing between competing hypotheses about a probability distribution, based on observed data from the distribution. It is a core topic in mathematical ….
Alternative hypothesis is that population average > 3. The hypothesis are always about the population parameters and never about the sample statistics.
When you perform a hypothesis test of a single population proportion p, you take a simple random sample from the population. You must meet the conditions for a binomial distribution which are: there are a certain number n of independent trials, the outcomes of any trial are success or failure, and each trial has the same probability of a success p.
Department of Education. Banigon Jr., Ricardo B. (2016). Statistics and Probability. Educational Resources Corporation. Quezon City, Philippines. Calaca, N. I. (2016). Statistics and Probability.