null hypothesis in excel

How to Do a T Test in Excel (2 Ways with Interpretation of Results)

The article will show you how to do a T Test in Excel. T-Tests are hypothesis tests that evaluate one or two groups’ means. Hypothesis tests employ sample data to infer population traits. In this lesson, we will look at the different types of T-Tests , and how to run T-Tests in Excel. We’ll go over both paired and two sample T-Tests , with detailed instructions on how to prepare your data, run the test, and interpret the findings.

Understanding how to use the T.TEST function in Excel will improve your ability to draw significant insights and make data-driven decisions, whether you’re a student, researcher, business analyst, or anybody else who works with data. Let’s say, you’re doing education research to assess the efficacy between traditional and new approaches. T-tests will guide you through providing the mean scores of students based on the approaches that they were taught. So that, you can make a decision based on the students’ performance.

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T Test.xlsx

T Test Type

There are basically two types of t-tests. They are:

• One-tailed t-test
• Two-tailed t-test

Each of them has 3 types. They are:

• Two sample equal variance
• Two sample unequal variance

We will show you the application of some of these types. The procedure of getting the results for all types of t-tests in Excel are the same. Let’s dig into some details and see how it can be done.

How to Do a T Test in Excel: 2 Effective Ways

1. using excel t.test or ttest function to do t test.

Here, we are going to show you how to determine the T Test result by using formulas. Excel has T.TEST and TTEST functions to operate t-test on different variables. Both functions work similarly. First, we will cover how to determine the t-test value of two sample variables with equal variance.

1.1 Two Sample Equal Variance T Test

In the dataset, you will see the prices of different laptops and smartphones. Here is a formula that performs a T Test on the prices of these products and returns the t-test result.

=T.TEST(B5:B14,C5:C14,2,2)

We set the 3rd argument of the function to 2 as we are doing a two tailed t-test on the dataset. The 4th argument should be 2 for a two sample equal variance t-test.

1.2 Paired T Test

Now, we are going to apply another formula to calculate the Paired T-Test . The following dataset shows the performance mark of some employees in two different criteria.

=T.TEST(C5:C13,D5:D13,2,1)

Note: The explanation of the results is described in the following sections.

2. Using Analysis Toolpak

The above tasks can be done with the Analysis Toolpak Add-in too. The Analysis Toolpak Add-in is not available in the ribbon by default. To initiate it,

• Go to the Options window first.
• Next, select Add-ins and click on the Go button beside the Manage section.
• After that, click OK .

• Thereafter, the Add-ins window will appear. Select Analysis Toolpak >> click OK again.

This Add-in will be added to the ribbon of the Data tab.

2.1 Two Sample Equal Variance T Test

We will do a two sample equal variance t-test using the Analysis Toolpak here. We used the dataset that contains the prices of laptops and smartphones. For this purpose,

• Click on the Data Analysis button from the ribbon of the Data tab.
• The Data Analysis features will appear. Select t-Test: Two Sample Assuming Equal Variances and click OK .

• After that, you need to set up the parameters for the t-test operation. Insert the Laptop and Smartphone prices as Variable 1 Range and Variable 2 Range Include the headings in the range and check Labels.
• Next, set the value of Hypothesized Mean Difference to 0 .
• Finally, select an Output option of your preference and click OK .

As we have chosen a New Worksheet for the outputs, we will see the results in a new sheet.

Now, let’s get to the discussion on the results.

Comments on Results

The output shows that the mean values for Laptops and Smartphones are 1608.85 and 1409.164 respectively. We can see from the Variances row that they are not precisely equal, but they are close enough to be assumed to have equal variances. The most relevant metric is the p-value .

The difference between means is statistically significant if the p-value is less than your significance level. Excel calculates p-values for one- and two-tailed T Tests .

One-tailed T Tests can detect only one direction of difference between means. A one-tailed test, for example, might only evaluate whether Smartphones have higher prices than Laptops . Two-tailed tests can reveal differences that are larger or smaller than. There are some other disadvantages to utilizing one-tailed testing, so I’ll continue with the conventional two-tailed results.

For our results, we’ll utilize P(T=t) two-tail, which is the p-value for the t-test’s two-tailed version. We cannot reject the null hypothesis because our p-value ( 0.095639932 ) is greater than the conventional significance level of 0.05 . The hypothesis that the population means differ is supported by our sample data. The mean price of Laptops is greater than the mean price of Smartphones’ .

The Analysis Toolpak operation also returns results for one-tailed t-test . Here, the one-tailed P value of two sample equal variance t-test is 1.734 .

2.2 Paired T Test

Similarly, you can find out the Paired t-Test result for the dataset containing employee performances. Just select the t-Test: Paired Two Samples for Mean when you open the Data Analysis window.

The result shows that the mean for the Workpace is 104 and the mean for the Efficiency is 96.56 .

The difference between means is statistically significant if the p-value is less than your significance level. For our results, we’ll utilize P(T=t) two-tail, which is the p-value for the t-test’s two-tailed version. We cannot reject the null hypothesis because our p-value ( 0.188 ) is greater than the conventional significance level of 0.05 . The hypothesis that the population means differ is supported by our sample data. In particular, the Workpace mean exceeds the Efficiency mean.

How to Interpret t-Test Results in Excel

Although we explained the results of the t-Test earlier, we didn’t show the proper interpretation. So here, I’ll show you the interpretation of the two sample equal variance t-test.

Let’s bring out the results again first.

• The mean of laptop prices = 1608.85
• The mean of smartphone prices = 1409.164

ii. Variance

• The variance of laptop prices = 77622.597
• The variance of smartphone prices = 51313.7904

iii. Observations

The number of observations for both laptops and smartphones are 10 .

iv. Pooled Variance

The samples’ average variance, calculated by pooling the variances of each sample.

The mathematical formula for this parameter is:

((No of observations of Sample 1-1)*(Variance of Sample 1) + (No of observations of Sample 2-1)*(Variance of Sample 2))/(No of observations of Sample 1 + No of observations of Sample 2 – 2)

So it becomes: ((10-1)*77622.59676+(10-1)*51313.7904)/(10+10-2) = 64468.19358

v. Hypothesized Mean Difference

We “hypothesize” that the number is the difference between the two population means. In this situation, we chose 0 because we want to see if the difference between the means of the two populations is zero.

It indicates the value of the Degrees of Freedom. Formula for this parameter is:

No of observations of Sample 1 + No of observations of Sample 2 – 2 = 10 + 10 – 2 = 18

vii. t Stat

The test statistic value of the t-Test operation.

The formula for this parameter is given below.

(Mean of Sample 1 – Mean of Sample 2)/(Square root of (Pooling Variance* (1/No of observations of Sample 1 + 1/No of observations of Sample 2)))

So it becomes: (1608.85 – 1409.164)/Sqrt(64468.19358 * (1/10 + 1/10)) = 1.758570846

viii. P(T<=t) two-tail

A two-tailed t-test’s p-value. This value can be found by entering t = 1.758570846 with 18 degrees of freedom into any T Score to P Value Calculator.

In this situation, the value of p is 0.095639932 . Because this is greater than 0.05 , we cannot reject the null hypothesis. This suggests that we lack adequate evidence to conclude that the two population means differ.

ix. t Critical two-tail

This is the test’s crucial value. A t Critical value Calculator with 18 degrees of freedom and a 95% confidence level can be used to calculate this number.

In this instance, the critical value is 2.10092204 . We cannot reject the null hypothesis because our test statistic t is less than this number. Again, we lack adequate information to conclude that the two population means are distinct.

Things to Remember

• Excel demands that your data be arranged in columns, with data from each group in a separate column. The first row should have labels or headers.
• Clearly state your null hypothesis (usually that there is no significant difference between the group means) and your alternative hypothesis (the opposite of the null hypothesis).
• As a result of the t-test, Excel returns the p-value. A little p-value (usually less than the specified alpha level) indicates that the null hypothesis may be rejected and that there is a substantial difference between the group means.

Frequently Asked Questions

1. Can I perform a t-test on unequal sample sizes in Excel?

Answer: Yes, you can use the T.TEST function to do a t-test on unequal sample sizes. When calculating the test statistic, Excel automatically accounts for unequal sample sizes.

2. What is the difference between a one-tailed and a two-tailed t-test?

Answer: A one-tailed t-test determines if the means of the two groups differ substantially in a given direction (e.g., greater or smaller). A two-tailed t-test looks for any significant difference, regardless of direction.

3. Can I calculate effect size in Excel for t-tests?

Answer: While there is no built-in tool in Excel to calculate effect size, you may manually compute Cohen’s d for independent t-tests and paired sample correlations for paired t-tests using Excel’s basic mathematical operations.

In the end, we can conclude that you will learn some basic ideas on how to do a t Test in Excel. If you have any questions or feedback regarding this article, please share them in the comment section. Your valuable ideas will enrich my Excel expertise and hence the content of my upcoming articles.

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Md. Meraz Al Nahian has worked with the ExcelDemy project for over 1.5 years. He wrote 140+ articles for ExcelDemy. He also solved a lot of user problems and worked on dashboards. He is interested in data analysis, advanced Excel, statistics, and dashboards. He also likes to explore various Excel and VBA applications. He completed his graduation in Electrical & Electronic Engineering from Bangladesh University of Engineering & Technology (BUET). He enjoys exploring Excel-related features to gain efficiency... Read Full Bio

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The Complete Guide: Hypothesis Testing in Excel

In statistics, a hypothesis test is used to test some assumption about a population parameter .

There are many different types of hypothesis tests you can perform depending on the type of data you’re working with and the goal of your analysis.

This tutorial explains how to perform the following types of hypothesis tests in Excel:

• One sample t-test
• Two sample t-test
• Paired samples t-test
• One proportion z-test
• Two proportion z-test

Let’s jump in!

Example 1: One Sample t-test in Excel

A one sample t-test is used to test whether or not the mean of a population is equal to some value.

For example, suppose a botanist wants to know if the mean height of a certain species of plant is equal to 15 inches.

To test this, she collects a random sample of 12 plants and records each of their heights in inches.

She would write the hypotheses for this particular one sample t-test as follows:

• H 0 :  µ = 15
• H A :  µ ≠15

Refer to this tutorial for a step-by-step explanation of how to perform this hypothesis test in Excel.

Example 2: Two Sample t-test in Excel

A two sample t-test is used to test whether or not the means of two populations are equal.

For example, suppose researchers want to know whether or not two different species of plants have the same mean height.

To test this, they collect a random sample of 20 plants from each species and measure their heights.

The researchers would write the hypotheses for this particular two sample t-test as follows:

• H 0 :  µ 1 = µ 2
• H A :  µ 1 ≠ µ 2

Example 3: Paired Samples t-test in Excel

A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.

For example, suppose we want to know whether a certain study program significantly impacts student performance on a particular exam.

To test this, we have 20 students in a class take a pre-test. Then, we have each of the students participate in the study program for two weeks. Then, the students retake a post-test of similar difficulty.

We would write the hypotheses for this particular two sample t-test as follows:

• H 0 :  µ pre = µ post
• H A :  µ pre ≠ µ post

Example 4: One Proportion z-test in Excel

A  one proportion z-test  is used to compare an observed proportion to a theoretical one.

For example, suppose a phone company claims that 90% of its customers are satisfied with their service.

To test this claim, an independent researcher gathered a simple random sample of 200 customers and asked them if they are satisfied with their service.

• H 0 : p = 0.90
• H A : p ≠ 0.90

Example 5: Two Proportion z-test in Excel

A two proportion z-test is used to test for a difference between two population proportions.

For example, suppose a s uperintendent of a school district claims that the percentage of students who prefer chocolate milk over regular milk in school cafeterias is the same for school 1 and school 2.

To test this claim, an independent researcher obtains a simple random sample of 100 students from each school and surveys them about their preferences.

• H 0 : p 1 = p 2
• H A : p 1  ≠ p 2

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Excel Tutorial: How To Do A Hypothesis Test In Excel

Introduction.

Welcome to our Excel tutorial on how to conduct a hypothesis test using Excel. Hypothesis testing is a crucial component of statistical analysis, allowing us to make inferences about a population based on sample data. Using Excel for hypothesis testing offers several advantages, including its familiarity, ease of use, and the ability to perform complex statistical calculations with just a few clicks.

Key Takeaways

• Hypothesis testing is essential for making inferences about a population based on sample data.
• Using Excel for hypothesis testing offers familiarity, ease of use, and the ability to perform complex statistical calculations.
• Organizing and formatting data correctly in Excel is crucial for hypothesis testing.
• Understanding the different types of hypothesis tests and selecting the appropriate test is important for accurate analysis.
• Interpreting the results of the hypothesis test and avoiding common mistakes is essential for making valid conclusions.

Setting up the data in Excel

When conducting a hypothesis test in Excel, it is crucial to properly organize and format your data in a spreadsheet. This will ensure accurate and reliable results.

• Start by opening a new Excel spreadsheet and entering your raw data into the cells. It is important to have a clear understanding of the variables you are working with and how they relate to each other.
• Label each column with a clear and descriptive header to identify the variables being tested. This will help you keep track of the data and make it easier to analyze.
• Arrange the data in a logical and organized manner, such as grouping similar data together and using separate columns for different variables.
• Check that the data is formatted correctly, especially if it includes dates, currency, or percentages. Use the appropriate formatting options in Excel to ensure the data is displayed accurately.
• Remove any unnecessary formatting, such as extra spaces or special characters, to avoid errors in the analysis process.
• Double-check for any missing or erroneous data entries, and make sure that the data is complete and accurate before proceeding with the hypothesis test.

Choosing the Appropriate Test in Excel

When conducting a hypothesis test in Excel, it's crucial to choose the right test for your specific scenario. Understanding the different types of hypothesis tests and how to select the appropriate one is essential for accurate and meaningful results.

Parametric Tests:

Nonparametric tests:, one-sample, two-sample, and paired tests:, goodness-of-fit tests:, chi-square tests:.

Choosing the right hypothesis test in Excel requires careful consideration of the nature of the data and the specific research question. Here are some key factors to consider when selecting the appropriate test:

• Understanding the Data: Determine whether the data is continuous or categorical, and whether it follows a specific distribution.
• Research Question: Clearly define the research question and the type of comparison or relationship being investigated.
• Sample Size: Consider the size of the sample and whether it meets the assumptions of the chosen test.
• Dependent or Independent Variables: Determine whether the variables are independent or related in some way, as this will impact the choice of test.
• Assumptions: Ensure that the chosen test aligns with any specific assumptions or conditions required for accurate results.

Conducting the hypothesis test

When it comes to conducting a hypothesis test in Excel, there are a few key steps to follow in order to ensure accurate results. These steps include using the Data Analysis Toolpak and inputting the necessary parameters for the test.

The Data Analysis Toolpak is a powerful add-in for Excel that provides a variety of data analysis tools, including the ability to conduct hypothesis tests. To access the Toolpak, simply go to the "Data" tab, click on "Data Analysis" in the Analysis group, and select "t-Test: Two-Sample Assuming Equal Variances" for a two-sample t-test, or "t-Test: Paired Two Sample for Means" for a paired t-test.

Once the Data Analysis Toolpak is open, you will need to input the necessary parameters for the hypothesis test. This includes selecting the appropriate variables for analysis, specifying the significance level, and choosing whether to perform a one-tailed or two-tailed test. It is important to carefully review and input the correct parameters to ensure the accuracy of the test results.

By using the Data Analysis Toolpak in Excel and inputting the necessary parameters for the hypothesis test, you can effectively conduct hypothesis tests and analyze your data with confidence.

Interpreting the results

After performing a hypothesis test in Excel, it is important to understand how to interpret the results and make conclusions based on the data.

Identify the test statistic:

Look at the p-value:, consider the confidence interval:, check for statistical significance:, reject or fail to reject the null hypothesis:, consider the practical significance:, communicate the findings:, common mistakes to avoid.

When conducting a hypothesis test in Excel, there are some common mistakes that researchers often make. By being aware of these pitfalls, you can ensure that your results are accurate and reliable.

One of the most common mistakes when doing a hypothesis test in Excel is misinterpreting the results. It's important to carefully analyze the output of the test and understand what it is telling you. Avoid jumping to conclusions without thoroughly examining the data and the significance level.

Another mistake to avoid is using the wrong test for the hypothesis you are trying to test. Excel offers a variety of hypothesis tests, such as t-tests, F-tests, and chi-squared tests, among others. It's crucial to select the appropriate test for your specific research question and data set. Using the wrong test can lead to inaccurate results and conclusions.

In conclusion, hypothesis testing in Excel is a crucial tool for making data-driven decisions in various fields, from business to science. By using Excel, we can effectively analyze data and draw meaningful conclusions about our hypotheses.

As with any skill, practice makes perfect . So, I encourage you to continue exploring and practicing hypothesis testing in Excel. There are numerous resources available online that provide additional guidance and examples to help you master this valuable technique.

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How to Do Hypothesis Tests With the Z.TEST Function in Excel

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Hypothesis tests are one of the major topics in the area of inferential statistics. There are multiple steps to conduct a hypothesis test and many of these require statistical calculations. Statistical software, such as Excel, can be used to perform hypothesis tests. We will see how the Excel function Z.TEST tests hypotheses about an unknown population mean.

Conditions and Assumptions

We begin by stating the assumptions and conditions for this type of hypothesis test. For inference about the mean we must have the following simple conditions:

• The sample is a simple random sample .
• The sample is small in size relative to the population . Typically this means that the population size is more than 20 times the size of the sample.
• The variable being studied is normally distributed.
• The population standard deviation is known.
• The population mean is unknown.

All of these conditions are unlikely to be met in practice. However, these simple conditions and the corresponding hypothesis test are sometimes encountered early in a statistics class. After learning the process of a hypothesis test, these conditions are relaxed in order to work in a more realistic setting.

Structure of the Hypothesis Test

The particular hypothesis test we consider has the following form:

• State the null and alternative hypotheses .
• Calculate the test statistic, which is a z -score.
• Calculate the p-value by using the normal distribution. In this case the p-value is the probability of obtaining at least as extreme as the observed test statistic, assuming the null hypothesis is true.
• Compare the p-value with the level of significance to determine whether to reject or fail to reject the null hypothesis.

We see that steps two and three are computationally intensive compared two steps one and four. The Z.TEST function will perform these calculations for us.

Z.TEST Function

The Z.TEST function does all of the calculations from steps two and three above. It does a majority of the number crunching for our test and returns a p-value. There are three arguments to enter into the function, each of which is separated by a comma. The following explains the three types of arguments for this function.

• The first argument for this function is an array of sample data. We must enter a range of cells that corresponds to the location of the sample data in our spreadsheet.
• The second argument is the value of μ that we are testing in our hypotheses. So if our null hypothesis is H 0 : μ = 5, then we would enter a 5 for the second argument.
• The third argument is the value of the known population standard deviation. Excel treats this as an optional argument

Notes and Warnings

There are a few things that should be noted about this function:

• The p-value that is output from the function is one-sided. If we are conducting a two-sided test, then this value must be doubled.
• The one-sided p-value output from the function assumes that the sample mean is greater than the value of μ we are testing against. If the sample mean is less than the value of the second argument, then we must subtract the output of the function from 1 to get the true p-value of our test.
• The final argument for the population standard deviation is optional. If this is not entered, then this value is automatically replaced in Excel’s calculations by the sample standard deviation. When this is done, theoretically a t-test should be used instead.

We suppose that the following data are from a simple random sample of a normally distributed population of unknown mean and standard deviation of 3:

1, 2, 3, 3, 4, 4, 8, 10, 12

With a 10% level of significance we wish to test the hypothesis that the sample data are from a population with mean greater than 5. More formally, we have the following hypotheses:

• H 0 : μ= 5
• H a : μ > 5

We use Z.TEST in Excel to find the p-value for this hypothesis test.

• Enter the data into a column in Excel. Suppose this is from cell A1 to A9
• Into another cell enter =Z.TEST(A1:A9,5,3)
• The result is 0.41207.
• Since our p-value exceeds 10%, we fail to reject the null hypothesis.

The Z.TEST function can be used for lower tailed tests and two tailed tests as well. However the result is not as automatic as it was in this case. Please see here for other examples of using this function.

• What Is a P-Value?
• Example of Two Sample T Test and Confidence Interval
• Hypothesis Test Example
• Hypothesis Test for the Difference of Two Population Proportions
• An Example of a Hypothesis Test
• Functions with the T-Distribution in Excel
• The Runs Test for Random Sequences
• How to Conduct a Hypothesis Test
• How to Use the NORM.INV Function in Excel
• Chi-Square Goodness of Fit Test
• What Is the Difference Between Alpha and P-Values?
• What Level of Alpha Determines Statistical Significance?
• How to Find Degrees of Freedom in Statistics
• Robustness in Statistics
• How to Use the STDEV.S Function in Excel
• Example of a Chi-Square Goodness of Fit Test

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How to Find Null and Alternative Hypothesis in Excel

Table of Contents

When conducting statistical analysis, it is essential to formulate a hypothesis that can be tested against the available data. The hypothesis serves as the foundation for making informed decisions and drawing conclusions. In this article, we will explore the process of finding null and alternative hypotheses in Excel, a widely used spreadsheet software. We will delve into the significance of these hypotheses, provide step-by-step instructions on how to create them, and offer valuable insights to enhance your understanding. So, let’s dive in!

Understanding Null and Alternative Hypotheses

Before we delve into the process of finding null and alternative hypotheses in Excel, it is crucial to understand their significance and how they relate to statistical analysis.

The null hypothesis, denoted as H 0 , represents the default assumption or the status quo. It states that there is no significant difference or relationship between the variables being studied. On the other hand, the alternative hypothesis, denoted as H 1 or H a , proposes an alternative explanation or relationship between the variables.

These hypotheses are essential in hypothesis testing, where we aim to determine whether the observed data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. By formulating these hypotheses, we can make informed decisions based on statistical evidence.

Step-by-Step Guide to Finding Null and Alternative Hypotheses in Excel

Now that we have a clear understanding of null and alternative hypotheses, let’s explore the step-by-step process of finding them in Excel.

Step 1: Define the Research Question

The first step in finding null and alternative hypotheses is to define the research question. Clearly articulate the problem you are trying to solve or the relationship you are trying to explore. This will guide the formulation of your hypotheses.

Step 2: Determine the Type of Hypothesis

Next, determine whether you are dealing with a one-tailed or two-tailed hypothesis. A one-tailed hypothesis predicts the direction of the relationship between variables, while a two-tailed hypothesis does not make any directional predictions.

Step 3: Formulate the Null Hypothesis

Based on the research question and the type of hypothesis, formulate the null hypothesis. The null hypothesis typically assumes no difference or no relationship between the variables being studied. It is often expressed as an equality statement or a statement of no effect.

For example, if you are investigating whether a new marketing campaign has a significant impact on sales, the null hypothesis could be: “The new marketing campaign has no significant effect on sales.”

Step 4: Formulate the Alternative Hypothesis

Once the null hypothesis is defined, formulate the alternative hypothesis. The alternative hypothesis proposes an alternative explanation or relationship between the variables. It is often expressed as an inequality statement or a statement of an effect.

Continuing with the previous example, the alternative hypothesis could be: “The new marketing campaign has a significant positive effect on sales.”

Step 5: Conduct Statistical Analysis in Excel

After formulating the null and alternative hypotheses, it is time to conduct statistical analysis in Excel to test these hypotheses. Excel offers various statistical functions and tools that can assist in this process.

For example, if you have a dataset of sales figures before and after the marketing campaign, you can use Excel’s t-test function to compare the means of the two samples and determine whether the difference is statistically significant.

Valuable Insights and Tips

While the above steps provide a general framework for finding null and alternative hypotheses in Excel, here are some valuable insights and tips to enhance your understanding:

• Ensure that your hypotheses are specific, measurable, and testable. This will make it easier to analyze the data and draw meaningful conclusions.
• Consider the sample size and statistical power when formulating your hypotheses. A larger sample size generally increases the likelihood of detecting a significant effect.
• Use Excel’s data analysis tools, such as regression analysis or ANOVA, to explore relationships between multiple variables and formulate more complex hypotheses.
• Remember that statistical significance does not necessarily imply practical significance. Consider the context and practical implications of your findings.

Frequently Asked Questions (FAQ)

Q: can i find null and alternative hypotheses for non-numerical data in excel.

A: Yes, Excel offers various functions and tools to analyze non-numerical data as well. For example, you can use Excel’s chi-square test function to test the independence of categorical variables and formulate hypotheses accordingly.

Q: How do I interpret the results of hypothesis testing in Excel?

A: Excel provides statistical outputs such as p-values, t-values, or F-values that can help interpret the results of hypothesis testing. A p-value less than the chosen significance level (e.g., 0.05) indicates that the data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

Q: Can I use Excel for advanced statistical analysis?

A: While Excel offers a range of statistical functions, it may not be suitable for advanced statistical analysis. Consider using specialized statistical software such as SPSS or R for complex analyses.

Formulating null and alternative hypotheses is a crucial step in statistical analysis. By defining these hypotheses, we can test the validity of assumptions and make informed decisions based on data. In this article, we explored the process of finding null and alternative hypotheses in Excel, providing step-by-step instructions and valuable insights. Remember to define the research question, determine the type of hypothesis, formulate the null and alternative hypotheses, conduct statistical analysis in Excel, and interpret the results. By following these steps and considering the tips provided, you can enhance your statistical analysis skills and draw meaningful conclusions from your data.

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Hypothesis Testing

So, a hypothesis is just a statement of theory.  It may or may not be true.  A drug company can claim that a new drug is better at decreasing blood pressure.   You may claim that the diet plan you created helps people lose more weight than a nationally known diet plan.  All these things are just statements – just hypotheses.

The hypothesis is the starting point.  From there, we have to test the hypothesis and reach a decision if the hypothesis is probably true or probably false.  Note the word “probably.”  There is always variation – so there is always a chance for you to make the wrong decision.  This month’s publication takes a look at the five steps involved in conducting a hypothesis test.

In this issue:

• The problem
• A brief pause for the standard normal distribution
• Formulate the null hypothesis and the alternative hypothesis
• Determine the significance level
• Collect the data and calculate the sample statistics
• Calculate the p value for the hypothesis test
• Compare the p value to the desired significance level

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The Problem

The average coating thickness is 5 mil.  You want to be sure that the coating thickness remains the same before you will approve the process change.

The team wants to perform a hypothesis test to prove that the average coating thickness will not change.  The team will go through the basic five steps of hypothesis testing:

The details of the five steps are shown below.  However, before those steps are covered, a review of the standard normal distribution is needed.  This will be required when we do some calculations.

A Brief Pause for the Standard Normal Distribution

We need to digress a moment here because we will need to make use of a special case of the normal distribution – when the average = 0 and the standard deviation = 1. This special case is called the standard normal distribution and is shown in Figure 1.

Figure 1: Standard Normal Distribution

For this distribution, the area under the curve from -∞ to +∞ is equal to 1.0. In addition, the area under the curve is proportional to the fraction of measurements that fall in that region. These two facts can used to help determine the fraction of measurements that fall above some value (such as a specification limit), below some value, or between two values.

z=  (x- μ)/σ

where x is some value, μ is the average, and σ is the standard deviation of the x values.  The value of z (the z score) is simply how many standard deviations a value, x, is from the average.

For example, suppose x is 1.5 standard deviations below the average.  In this case, z = -1.5.  The area below z = -1.5 is the percentage of x values that are more than 1.5 standard deviations below the average.  For z = -1.5, that area is 6.68% as is shown in Figure 1.   If z = 1.5, then the area above z = 1.5 is the percentage of x values that are more than 1.5 standard deviations above the average.  This area is also 6.68%.

To find the percentage of data within z = -1.5 and z = 1.5, you simply use the fact that the area under the curve is 100%, so the percentage of data between the two z values is 100 – 6.68 – 6.68 = 86.64%.  You can determine these percentages from a table of z values (see our publication on the normal distribution ) or by using Excel’s NORMSDIST function.

These percentages can also be viewed as probabilities, e.g., the probability of getting a result that is less than -1.5 standard deviations below the average is 0.0668.  We will make use of this knowledge below.  Now back to the steps in hypothesis testing.

Step 1: Formulate the Null Hypothesis and Alternative Hypothesis

So the null hypothesis (H 0 ) is that the process change will not impact the average coating thickness; the average coating thickness (μ) will remain at 5.  This is usually written as:

Now for the alternative hypothesis, which is denoted by H 1 .  The alternative hypothesis is that the process change will have an effect on the average coating thickness and the average coating thickness will not equal 5.  This is usually written as:

This is called a two-sided hypothesis test since you are only interested if the mean is not equal to 5.  You can have one-sided tests where you want the mean to be greater than or less than some value.

Step 2: Determine the Significance Level You Want

The significance level is important in hypothesis testing.  It is the probability of rejecting the null hypothesis when it is true.  This probability is denoted by α.  Typical values of  α include 0.05 and 0.01.  You decide that you want α to be 0.05.  This means that there is only a 5% of chance of rejecting the null hypothesis when it is actually true.

Step 3: Collect the Data and Calculate the Sample Statistics

X   = average coating thickness = 5.06

s = standard deviation of the coating thickness = 0.20

We have our statistics.  How do you decide to accept or reject the null hypothesis?  The way you do this is to assume that the null hypothesis is true and then determine the probability (p value) of getting this sample average.  If the p value is large, it means that there is large probability of getting an average thickness of 5.06 with a standard deviation of 0.20 when the null hypothesis is true and you will accept that the null hypothesis is probably true.  But if the probability of getting these statistics is small, you will assume that the null hypothesis is probably not true and reject it in favor the alternative hypothesis.

Step 4: Calculate the p Value

To determine this probability, you will need to consider your sampling distribution.    The distribution of sample averages tends to be normal when the sample size is large enough.  We will use this assumption here.  So, your sampling distribution is represented by all the possible sample averages of sample size 25 from the population of coating thicknesses.  This normal distribution is shown in Figure 2.

Figure 2: Normal Distribution for Sample Averages

The highest point on the curve is the average.  The population average of the sample averages (μ X ) is equal to the population average, μ, so we have just used μ in Figure 1.  The standard deviation of the sample averages is denoted by σ X .

To be able to draw your sampling distribution, you need to know μ X   and  σ X .  Since you assumed that the null hypothesis is true, μ X   = 5.0.  The standard deviation of the sample averages is given by:

where σ is the population standard deviation and n is the sample size.

You don’t know what the population standard deviation is, but you have an estimate from the sample statistics.  The standard deviation of the 25 samples was 0.2.  You can use this as the population standard deviation.

σ X =σ/√n =  s/√n=0.2/√25=0.04

Now you can draw the sampling distribution and add the sample average as shown in Figure 3.

Figure 3: Sampling Distribution

Now we return to the z score.  Remember, the z score is a measure of how many standard deviations the sample average ( X  )is from the population average (μ).   For this example, the z value is calculated as:

z=  ( X -μ)/σ X =(5.06-5)/.04=.06/.04=1.5

So, 5.06 is 1.5 standard deviations away from the average.    As shown above, the probability of getting a result that is 1.5 standard deviations away from the average is 0.0668.  Remember, this a two-side test, so you didn’t care if the difference was above or below the average.  So, the probability of getting an average that is more than 1.5 standard deviations away from the average is 2(0.0668) = 0.1336 or 13.36%.  This is the p value:

p value = 0.1336

Remember what the p value represents.  You assumed that the null hypothesis is true.  The p value is the probability of getting this result (or a more extreme result) if the null hypothesis is true.

Step 5:  Compare the p value to the Desired Significance Level

In step 2, we set the significance level at 0.05.  Since our p value is greater than this, we conclude that the coating thickness was not impacted by the process change.  We accept the null hypothesis as probably being true.  If the p value had been less than 0.05, we would rejected the null hypothesis and said that the process change did impact the coating thickness.

This newsletter has taken a look at how to perform hypothesis testing.  The five steps are:

• Determine the significance level you want

The normal distribution was used to demonstrate how hypothesis testing is done.  You will not always be dealing with the normal distribution but the process is essentially the same.  One item that is still to be discussed is how to select the sample size.  This will be the subject of a later publication.

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Thanks so much for reading our SPC Knowledge Base. We hope you find it informative and useful. Happy charting and may the data always support your position.

Dr. Bill McNeese BPI Consulting, LLC

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This example teaches you how to perform a single factor ANOVA (analysis of variance) in Excel . A single factor or one-way ANOVA is used to test the null hypothesis that the means of several populations are all equal.

Below you can find the salaries of people who have a degree in economics, medicine or history.

To perform a single factor ANOVA , execute the following steps.

1. On the Data tab, in the Analysis group, click Data Analysis.

Note: can't find the Data Analysis button? Click here to load the Analysis ToolPak add-in .

2. Select Anova: Single Factor and click OK.

3. Click in the Input Range box and select the range A2:C10.

4. Click in the Output Range box and select cell E1.

5. Click OK.

Conclusion: if F > F crit, we reject the null hypothesis. This is the case, 15.196 > 3.443. Therefore, we reject the null hypothesis. The means of the three populations are not all equal. At least one of the means is different. However, the ANOVA does not tell you where the difference lies. You need a t-Test to test each pair of means.

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How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =,  ≤, ≥ some value

H A  (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data  does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

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