hypothesis test on ti 84

• Hypothesis Testing using the Z-Test on the TI-83 Plus, TI-84 Plus, TI-89, and Voyage 200

The TI-83 Plus and TI-84 Plus are optimized for performing many tasks in statistics, and one of their most powerful features is the ability to perform a variety of tests of statistical significance. With the statistics package installed, the TI-89, TI-92 Plus, and Voyage 200 also have much of this capability. This tutorial demonstrates how to use your graphing calculator to solve basic hypothesis testing problems such as the following using the Z-Test:

A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x̄ = 540. Given that the average score of all high school seniors on the SAT is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher?

Before beginning the calculations, it is necessary to come up with specific hypotheses for the tests and choose a level of significance. In inferential statistics, there are two hypothesis, the null hypothesis, and the alternative hypothesis. The null hypothesis, denoted H₀, is always that the statistic measures of the treated group (in this case students given a pill) is the same as that for the general population. Since we are only interested in whether or not the pill has a positive effect, we are doing a one-tailed Z-Test, and our null hypothesis is:

H₀: μ <= μ₀

Where μ is the true mean (as opposed to sample mean) of scores of students in the treatment group. μ₀ refers to the known population mean, in this case 510. The alternative hypothesis H 1 is what we expect if the treatment does have an effect on the population, and is always the opposite of the alternative hypothesis. Our alternative hypothesis is:

H₁: μ > μ₀

Finally, we have to choose a level of significance (α) for our test. It is possible that even if the treatment has no effect, we could get a mean score of 540. This seems unlikely and the chances of this happening goes down with the more subjects in the study, but the purpose of hypothesis testing is first of all to avoid coming to the wrong conclusion. The level of significance is a threshold probability below which we say that we have found statistical evidence. It is considered good practice to choose this beforehand so that the statistician doesn’t change α after wards in order to “find” statistical evidence where there is none. For most problems, a level of significance is:

α = .05

This means that if we find there is less than a 5% chance that the sample mean is higher than 540 by chance alone, we will conclude statistical significance.

Performing a Z-Test on the TI-83 Plus and TI-84 Plus

From the home screen, press STAT ▶ ▶ to select the TESTS menu. “Z-Test” should already be selected, so press ENTER to be taken to the Z-Test menu.

Now select the desired settings and values. While it is possible to use a list to store a set of scores from which your calculator can determine the sample data, this problem doesn’t give individual scores, so make sure STATS is selected and press ENTER .

Enter the data given in the problem, μ₀ = 510, σ = 100, x̄ = 540, and n = 50. Finally, make sure to select >μ₀ for the alternative hypothesis.

There are now two options for the output of the Z-Test: “Calculate” displays the z-score (the number of standard deviations x̄ is above or below the mean) and then the corresponding p-value, the probability of getting such a sample by luck alone.

“Draw” draws a normal distribution graph and displays the z-score and p-value at the bottom of the screen.

We have z = 2.12 and p = .017 , which means that there is a 1.7% chance of seeing such a variation in sample mean by chance alone. Since p<α, we can conclude that there is significant evidence that the treatment group is different from the general population. Assuming good experimental practices, this implies (but does not prove) that taking the pill improves students' Math SAT scores. Note that this does not necessarily mean the pill improves concentration and problem solving skills as claimed-although these may be skills important for scoring higher on the Math SAT, this is a separate claim.

Performing a Z-Test on the TI-89, TI-92 Plus, and Voyage 200

Before you begin, it is necessary to have the proper software on your device. If you have a TI-89 Titanium or other newer calculator, then you should have a Stats/List Editor icon on your Apps screen. Otherwise, you should have a Stats/List Editor application in your Flash Apps folder. (Reached by pressing APPS then ENTER ). If you don’t have this software or you aren’t sure, you can download it here .

Once you are in the Stats/List Editor app, press 2nd F1 (F6) to enter the tests menu. Z-Test should already be selected, so press ENTER to confirm. You will be prompted for the data input method. Data uses a list containing the of scores from which your calculator can determine the sample data, this problem doesn’t give individual scores, so make sure STATS is selected and press ENTER .

Enter the data given in the problem, μ₀ = 510, σ = 100, x̄ = 540, and n = 50. Finally, make sure to select μ > μ₀ for the alternative hypothesis.

There are two options for the output of the Z-Test. Selecting “Results: Calculate” displays the z-score (the number of standard deviations x̄ is above or below the mean) and then the corresponding p-value, the probability of getting such a sample by luck alone.

“Results: Draw” draws a normal distribution graph and displays the z-score and p-value at the bottom of the screen.

We have z = 2.12 and p = .017 , which means that there is a 1.7% chance of seeing such a variation in sample mean by chance alone. Since p<α, we can conclude that there is significant evidence that the treatment group is different from the general population. As before, this implies (but does not prove) that taking the pill improves students' Math SAT scores.

You might also like:

• Transferring Spreadsheets Between Microsoft Excel and your TI-83+, TI-84+, TI-89, TI-92+, or Voyage 200
• Video: Using Variables on Your TI Graphing Calculator
• Quick Tip: How to Clear Variables on the TI-89, TI-92 Plus, and Voyage 200

One Response to Hypothesis Testing using the Z-Test on the TI-83 Plus, TI-84 Plus, TI-89, and Voyage 200

Leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Notice: It seems you have Javascript disabled in your Browser. In order to submit a comment to this post, please copy this code and paste it along with your comment: 4ea202fb09a9e1194ec521116b85bc14_3a0

• Search for:

Calcblog Newswire

Recently popular.

• SAT Test Prep #1: Mean, Mode, and Median on the TI-83 Plus, TI-84 Plus, and TI-89
• How to Enter Logarithms on Your Graphing Calculator
• Business and Finance Math #2: Calculating the Effective Annual Rate (EAR) on Your TI BA II Plus or HP 12c
• Business and Finance Math #4: Continuous Compounding on the TI BA II Plus & HP 12c

Calculators

• No categories

Visit Our Sponsors

© MMXIII | Legal | Sitemap

The Tech Edvocate

• Advertisement
• Home Page Five (No Sidebar)
• Home Page Four
• Home Page Three
• Home Page Two
• Icons [No Sidebar]
• Left Sidbear Page
• Lynch Educational Consulting
• My Speaking Page
• Newsletter Sign Up Confirmation
• Newsletter Unsubscription
• Page Example
• Privacy Policy
• Protected Content
• Request a Product Review
• Shortcodes Examples
• Terms and Conditions
• The Edvocate
• The Tech Edvocate Product Guide
• Write For Us
• Dr. Lynch’s Personal Website
• The Edvocate Podcast
• Assistive Technology
• Child Development Tech
• Early Childhood & K-12 EdTech
• EdTech Futures
• EdTech News
• EdTech Policy & Reform
• EdTech Startups & Businesses
• Higher Education EdTech
• Online Learning & eLearning
• Parent & Family Tech
• Personalized Learning
• Product Reviews
• Tech Edvocate Awards
• School Ratings

Best Practices for Multicultural Marketing

Ultra luxury generation divide: courting the next generation’s loyalty, mastering the art of email calls-to-action, the power of livestream marketing: engaging audiences and creating buzz, unlock business success through employee-driven growth, 3 emerging influencer trends that marketers should watch, ethical marketing: building trust and consumer engagement in the digital age, 5 keys to an effective crisis communications plan, lgbtqia+ community supports brands that support them, how ai is transforming the business of advertising, how to calculate test statistic on ti-84.

When conducting a hypothesis test, one of the critical steps is calculating the test statistic. A powerful yet user-friendly tool, the TI-84 graphing calculator, can help you do this quickly and accurately. In this article, we will discuss how to calculate a test statistic on a TI-84 calculator.

Step-by-Step Instructions:

1. Turn on your TI-84 calculator.

2. Press the “STAT” button located on the left side of the calculator to access the statistical modes.

3. Select “TESTS” from the displayed menu using the right arrow key.

4. Choose the type of hypothesis test you would like to perform. The most common tests include:

– 1-PropZTest for a proportion

– 2-PropZTest for comparing proportions from two independent samples

– T-Test for comparing means from one sample (with unknown population standard deviation)

– 2-SampTTest for comparing means from two independent samples (with unknown population standard deviations)

5. Once you have selected your desired test, press Enter to access data input prompts.

6. Input the required data values by pressing the corresponding arrow keys and then entering each value followed by Enter.

For instance:

– For 1-sample tests: input sample size (n), sample mean or proportion (e.g., x̄ or p̂), null hypothesis value (μ₀ or p₀), and sample standard deviation (s) if needed

– For 2-sample tests: input sample sizes (n₁ and n₂), sample means or proportions (x̄₁ and x̄₂ or p̂₁ and p̂₂), hypothesized difference in population means or proportions (μ₁ – μ₂ or p₁ – p₂), and sample standard deviations if needed

7. Choose an alternative hypothesis for your test using the arrow keys: lower-tailed test (μ > μ₀ or p > p₀), upper-tailed test (μ < μ₀ or p < p₀), or two-tailed test (μ ≠ μ₀ or p ≠ p₀). Press Enter to confirm your selection.

8. Press the “CALCULATE” button (usually scrolling down will bring you to the ‘Calculate’ option) and press Enter. The calculator will now calculate the test statistic and display it on the screen, along with the corresponding P-value.

9. Interpret your results by comparing the P-value with your chosen significance level (e.g., α = 0.05). A smaller P-value indicates stronger evidence against the null hypothesis, while a larger P-value suggests insufficient evidence for rejecting the null hypothesis.

Conclusion :

Calculating a test statistic on a TI-84 calculator is a straightforward process that can help you streamline your statistical analyses. By following these simple steps, you can quickly and accurately evaluate your hypothesis tests, enhancing your understanding of complex statistical concepts and making informed decisions based on data.

4 Ways to Grow Strawberries

How to calculate texas franchise tax.

Matthew Lynch

Related articles more from author.

How to calculate c.g.p.a

How to Calculate the Mode

How to calculate gain or loss on stock

How to Calculate Sales Percentage

How to calculate box fill

How to calculate correlation coefficient on excel

MathBootCamps

T-test for the mean using a ti83 or ti84 calculator (p-value method).

Do people tend to spend more than 2 hours on a computer every day? Can you say that the mean age of a college freshman in your state is not 18 years old? These are the types of questions that can be answered using collected data and a t-test for the mean. In this guide, you will see how you can use a TI83 or TI84 calculator to perform this test using the p-value method.

[adsenseWide]

We will use an example to see how this process works. For this example, assume that the requirements for a hypothesis test for the mean are met (randomly selected sample, independent observations, large population size).

Example: performing a t-test on the calculator

Suppose that a marketing firm believes that people who are planning to purchase a new TV spend more than 7 days researching their purchase. They conduct a survey of 32 people who had recently purchased a TV and found that the mean time spent researching the purchase was 7.8 days with a standard deviation of 3.9 days. At a significance level of 0.05, does this survey provide evidence to support the firm’s belief?

Step 1: Write the null and alternative hypotheses

The null hypothesis is the equality* statement using the same value:

Step 2: Calculate the p-value using your calculator and the correct test

1. Press [STAT] then go the the TESTS menu.

2. Select “2. T-test”. Make sure that you highlight Stats and press [ENTER] if your screen looks different from this.

3. Enter the values and select the correct tail for the test.

4. Highlight Calculate and press [ENTER].

Step 3: Compare the p-value to the significance level alpha and make your decision

To make the decision, use the decision rule:

In this problem:

Step 4: Interpret your decision in terms of the problem

So, we are saying that there is not enough evidence that the population mean is greater than 7. In context, we are saying:

This sample does not provide evidence that the mean time spent researching a new TV purchase is more than 7 days.

Although our sample mean was in fact larger than 7, it wasn’t quite enough to suggest that this is true for the entire population. Remember, in hypothesis testing, that is what we are trying to determine – is the sample enough to say that the hypothesis holds for the entire population?

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 11.

• When to use z or t statistics in significance tests
• Example calculating t statistic for a test about a mean
• Calculating the test statistic in a t test for a mean

Using TI calculator for P-value from t statistic

• Using a table to estimate P-value from t statistic
• Calculating the P-value in a t test for a mean
• Comparing P-value from t statistic to significance level
• Making conclusions in a t test for a mean
• Free response example: Significance test for a mean

Want to join the conversation?

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Video transcript

G | Notes for the TI-83, 83+, 84, 84+ Calculators

• [ ] represents yellow command or green letter behind a key
• < > represents items on the screen

To write in scientific notation Numbers in scientific notation are expressed on the TI-83, 83+, 84, and 84+ using E notation, such that...

• 4.321 E 4 = 4 .321 × 10 4 4 .321 × 10 4
• 4.321 E –4 = 4 .321 × 10 –4 4 .321 × 10 –4

Calculator receiving information

• Use the arrows to navigate to and select <RECEIVE> .

Calculator sending information

• Press the appropriate number or letter.
• Use the up and down arrows to access the appropriate item.
• Press the right arrow to navigate to and select <TRANSMIT> .

ERROR 35 LINK generally means that the cables have not been inserted far enough.

Manipulating One-Variable Statistics

These directions are for entering data using the built-in statistical program.

Enter data. Data values go into [L1] . (You may need to arrow over to [L1] ).

• Continue in the same manner until all data values are entered.

In [L2] , enter the frequencies for each data value in [L1] .

• Navigate to <CALC> .
• The statistics should be displayed. You may arrow down to get remaining statistics. Repeat as necessary.

Drawing Histograms

We will assume that the data are already entered.

We will construct two histograms with the built-in [STAT PLOT] application. In the first method, we will use the default ZOOM. The second method will involve customizing a new graph.

• Use the arrows to navigate to <Xlist> .
• Use the arrows to navigate to <Freq> .
• Use the arrows to turn off the remaining plots.
• Be sure to deselect or clear all equations before graphing.

To deselect equations

• Continue until all equations are deselected.

To clear equations

• Repeat until all equations are deleted.

To draw default histogram

• The histogram will display with a window automatically set.

To draw a custom histogram

• X min = –2.5 X min = –2.5
• X max = 3.5 X max = 3.5
• X s c l = 1 X s c l = 1 (width of bars)
• Y min = 0 Y min = 0
• Y max = 10 Y max = 10
• Y s c l = 1 Y s c l = 1 (spacing of tick marks on y -axis)
• X r e s = 1 X r e s = 1

To draw box plots

• Be sure to deselect or clear all equations before graphing using the method mentioned above.

Linear Regression

Sample data.

The following data are real. The percent of declared ethnic minority students at De Anza College for selected years from 1970–1995 is indicated in the following table.

The TI-83 has a built-in linear regression feature, which allows the data to be edited. The x -values will be in [L1] ; the y -values in [L2] .

To enter data and perform linear regression

To display the correlation coefficient

The display will show the following information

• a = –3176.909
• r 2 = 0.924

This means the Line of Best Fit (Least Squares Line) is:

• y = –3176.909 + 1.617 x
• % = –3176.909 + 1.617 (year #)

The correlation coefficient is r = 0.961.

To see the scatter plot

• Navigate to the first picture.
• Navigate to <Xlist> .
• Navigate to <Ylist> .
• X min = 1970 X min = 1970
• X max = 2000 X max = 2000
• X s c l = 10 X s c l = 10 (spacing of tick marks on x -axis)
• Y min = − 0.05 Y min = − 0.05
• Y max = 60 Y max = 60
• Y s c l = 10 Y s c l = 10 (spacing of tick marks on y -axis)
• Be sure to deselect or clear all equations before graphing, using the instructions above.

To see the regression graph

• Navigate to <EQ> .

To see the residuals and use them to calculate the critical point for an outlier

• n n = number of pairs of data
• SSE SSE = sum of the squared errors
• Verify that the calculator displays 7.642669563. This is the critical value.
• Compare the absolute value of each residual value in [L3] to 7.64. If the absolute value is greater than 7.64, then the ( x, y ) corresponding point is an outlier. In this case, none of the points is an outlier.

TI-83, 83+, 84, 84+ instructions for distributions and tests

Distributions.

Access DISTR for Distributions .

For technical assistance, visit the Texas Instruments website at http://www.ti.com and enter your calculator model into the search box.

Binomial Distribution

• binompdf( n , p , x ) corresponds to P ( X = x )
• binomcdf( n , p , x ) corresponds to P (X ≤ x)
• To see a list of all probabilities for x : 0, 1, . . . , n , leave off the " x " parameter.

Poisson Distribution

• poissonpdf(λ, x ) corresponds to P ( X = x )
• poissoncdf(λ, x ) corresponds to P ( X ≤ x )

Continuous Distributions (general)

• − ∞ − ∞ uses the value –1EE99 for left bound

Normal Distribution

• normalpdf( x , μ , σ ) yields a probability density function value, only useful to plot the normal curve, in which case " x " is the variable
• normalcdf(left bound, right bound, μ , σ ) corresponds to P (left bound < X < right bound)
• normalcdf(left bound, right bound) corresponds to P (left bound < Z < right bound) – standard normal
• invNorm( p , μ , σ ) yields the critical value, k : P ( X < k ) = p
• invNorm( p ) yields the critical value, k : P ( Z < k ) = p for the standard normal

Student's t -Distribution

• tpdf( x , df ) yields the probability density function value, only useful to plot the student- t curve, in which case " x " is the variable)
• tcdf(left bound, right bound, df ) corresponds to P (left bound < t < right bound)

Chi-square Distribution

• Χ 2 pdf( x , df ) yields the probability density function value, only useful to plot the chi 2 curve, in which case " x " is the variable
• Χ 2 cdf(left bound, right bound, df ) corresponds to P (left bound < Χ 2 < right bound)

F Distribution

• Fpdf( x , dfnum , dfdenom ) yields the probability density function value, only useful to plot the F curve, in which case " x " is the variable
• Fcdf(left bound,right bound, dfnum , dfdenom ) corresponds to P (left bound < F < right bound)

Tests and Confidence Intervals

Access STAT and TESTS .

For the confidence intervals and hypothesis tests, you may enter the data into the appropriate lists and press DATA to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT once in the appropriate tests.

Confidence Intervals

• ZInterval is the confidence interval for mean when σ is known.
• TInterval is the confidence interval for mean when σ is unknown; s estimates σ.
• 1-PropZInt is the confidence interval for proportion.

The confidence levels should be given as percents (e.g., enter " 95 " or " .95 " for a 95 percent confidence level).

Hypothesis Tests

• Z-Test is the hypothesis test for single mean when σ is known.
• T-Test is the hypothesis test for single mean when σ is unknown; s estimates σ.
• 2-SampZTest is the hypothesis test for two independent means when both σs are known.
• 2-SampTTest is the hypothesis test for two independent means when both σs are unknown.
• 1-PropZTest is the hypothesis test for a single proportion.
• 2-PropZTest is the hypothesis test for two proportions.
• Χ 2 -Test is the hypothesis test for independence.
• Χ 2 GOF-Test is the hypothesis test for goodness-of-fit (TI-84+ only).
• LinRegTTEST is the hypothesis test for Linear Regression (TI-84+ only).

Input the null hypothesis value in the row below " Inpt ." For a test of a single mean, " μ∅ " represents the null hypothesis. For a test of a single proportion, " p∅ " represents the null hypothesis. Enter the alternate hypothesis on the bottom row.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Statistics
• Publication date: Mar 27, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/statistics/pages/1-introduction
• Section URL: https://openstax.org/books/statistics/pages/g-notes-for-the-ti-83-83-84-84-calculators

© Jan 23, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

How to Perform a Paired Samples t-test on a TI-84 Calculator

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.

This tutorial explains how to conduct a paired t-test on a TI-84 calculator.

Example: Paired samples t-test on a TI-84 Calculator

Researchers want to know if a new fuel treatment leads to a change in the average mpg of a certain car. To test this, they conduct an experiment in which they measure the mpg of 11 cars with and without the fuel treatment.

Since each car receives the treatment, we can conduct a paired t-test in which each car is paired with itself to determine if there is a difference in average mpg with and without the fuel treatment.

Perform the following steps to conduct a paired t-test on a TI-84 calculator.

Step 1: Input the data.

First, we will input the data values for both samples. Press   Stat   and then press   EDIT  . Enter the following values for the control group (no fuel treatment) in column L1 and the values for the treatment group variable (received fuel treatment) in column L2, followed by the difference between these two values in column L3.

Note:  At the top of the third column, highlight L3. Then press   2nd   and   1   to create L1, followed by a minus sign, then press  2nd   and   2   to create L2. Then press  Enter . Each of the values in column L3 will automatically populate using the formula L1-L2.

Step 2: Perform the paired t-test.

To perform the paired t-test, we will simply perform a t-test on column L3, which contains the values for the paired differences.

Press  Stat . Scroll over to TESTS . Scroll down to 2:T-Test and press ENTER .

The calculator will ask for the following information:

• Inpt:  Choose whether you are working with raw data (Data) or summary statistics (Stats). In this case, we will highlight Data and press  ENTER .
• μ 0 : The mean difference to be used in the null hypothesis. We will type 0 and press   ENTER .
• List: The list that contains the differences between the two samples. We will type L3 and press   ENTER . Note: To get L3 to appear, press  2nd  and then press  3 .
• Freq:  The frequency. Leave this set to 1.
• μ :The alternative hypothesis to be used. Since we are performing a two-tailed test, we will highlight  ≠ μ 0  and press  ENTER . This indicates that our alternative hypothesis is μ≠0. The other two options would be used for left-tailed tests (0) and right-tailed tests (>μ 0 ) .

Lastly, highlight Calculate and press  ENTER .

Step 3: Interpret the results.

Our calculator will automatically produce the results of the one-sample t-test:

Here is how to interpret the results:

• μ≠0 : This is the alternative hypothesis for the test.
• t=-1.8751 : This is the t test-statistic. 
• p=0.0903 : This is the p-value that corresponds to the test-statistic.
• x =-1.5455 . This is the mean difference of group 1 – group 2.
• s x =2.7336 . This is the standard deviation of the differences.
• n=11 : This is the total number of paired samples.

Because the p-value of the test (0.0903) is not less than 0.05, we fail to reject the null hypothesis.

This means we do not have sufficient evidence to say that there is any difference between the average mpg of the two groups. That is, we do not have sufficient evidence to say that the fuel treatment affects mpg.

How to Create and Interpret Box Plots in Excel

How to calculate class width in excel, related posts, how to normalize data between -1 and 1, how to interpret f-values in a two-way anova, how to create a vector of ones in..., vba: how to check if string contains another..., how to determine if a probability distribution is..., what is a symmetric histogram (definition & examples), how to find the mode of a histogram..., how to find quartiles in even and odd..., how to calculate sxy in statistics (with example), how to calculate sxx in statistics (with example).

Statistics Made Easy

5 Tips for Interpreting P-Values Correctly in Hypothesis Testing

Hypothesis testing is a critical part of statistical analysis and is often the endpoint where conclusions are drawn about larger populations based on a sample or experimental dataset. Central to this process is the p-value. Broadly, the p-value quantifies the strength of evidence against the null hypothesis. Given the importance of the p-value, it is essential to ensure its interpretation is correct. Here are five essential tips for ensuring the p-value from a hypothesis test is understood correctly. 

1. Know What the P-value Represents

First, it is essential to understand what a p-value is. In hypothesis testing, the p-value is defined as the probability of observing your data, or data more extreme, if the null hypothesis is true. As a reminder, the null hypothesis states no difference between your data and the expected population. 

For example, in a hypothesis test to see if changing a company’s logo drives more traffic to the website, a null hypothesis would state that the new traffic numbers are equal to the old traffic numbers. In this context, the p-value would be the probability that the data you observed, or data more extreme, would occur if this null hypothesis were true. 

Therefore, a smaller p-value indicates that what you observed is unlikely to have occurred if the null were true, offering evidence to reject the null hypothesis. Typically, a cut-off value of 0.05 is used where any p-value below this is considered significant evidence against the null. 

2. Understand the Directionality of Your Hypothesis

Based on the research question under exploration, there are two types of hypotheses: one-sided and two-sided. A one-sided test specifies a particular direction of effect, such as traffic to a website increasing after a design change. On the other hand, a two-sided test allows the change to be in either direction and is effective when the researcher wants to see any effect of the change. 

Either way, determining the statistical significance of a p-value is the same: if the p-value is below a threshold value, it is statistically significant. However, when calculating the p-value, it is important to ensure the correct sided calculations have been completed. 

Additionally, the interpretation of the meaning of a p-value will differ based on the directionality of the hypothesis. If a one-sided test is significant, the researchers can use the p-value to support a statistically significant increase or decrease based on the direction of the test. If a two-sided test is significant, the p-value can only be used to say that the two groups are different, but not that one is necessarily greater. 

3. Avoid Threshold Thinking

A common pitfall in interpreting p-values is falling into the threshold thinking trap. The most commonly used cut-off value for whether a calculated p-value is statistically significant is 0.05. Typically, a p-value of less than 0.05 is considered statistically significant evidence against the null hypothesis. 

However, this is just an arbitrary value. Rigid adherence to this or any other predefined cut-off value can obscure business-relevant effect sizes. For example, a hypothesis test looking at changes in traffic after a website design may find that an increase of 10,000 views is not statistically significant with a p-value of 0.055 since that value is above 0.05. However, the actual increase of 10,000 may be important to the growth of the business. 

Therefore, a p-value can be practically significant while not being statistically significant. Both types of significance and the broader context of the hypothesis test should be considered when making a final interpretation. 

4. Consider the Power of Your Study

Similarly, some study conditions can result in a non-significant p-value even if practical significance exists. Statistical power is the ability of a study to detect an effect when it truly exists. In other words, it is the probability that the null hypothesis will be rejected when it is false. 

Power is impacted by a lot of factors. These include sample size, the effect size you are looking for, and variability within the data. In the example of website traffic after a design change, if the number of visits overall is too small, there may not be enough views to have enough power to detect a difference. 

Simple ways to increase the power of a hypothesis test and increase the chances of detecting an effect are increasing the sample size, looking for a smaller effect size, changing the experiment design to control for variables that can increase variability, or adjusting the type of statistical test being run.

5. Be Aware of Multiple Comparisons

Whenever multiple p-values are calculated in a single study due to multiple comparisons, there is an increased risk of false positives. This is because each individual comparison introduces random fluctuations, and each additional comparison compounds these fluctuations. 

For example, in a hypothesis test looking at traffic before and after a website redesign, the team may be interested in making more than one comparison. This can include total visits, page views, and average time spent on the website. Since multiple comparisons are being made, there must be a correction made when interpreting the p-value. 

The Bonferroni correction is one of the most commonly used methods to account for this increased probability of false positives. In this method, the significance cut-off value, typically 0.05, is divided by the number of comparisons made. The result is used as the new significance cut-off value.  Applying this correction mitigates the risk of false positives and improves the reliability of findings from a hypothesis test. 

In conclusion, interpreting p-values requires a nuanced understanding of many statistical concepts and careful consideration of the hypothesis test’s context. By following these five tips, the interpretation of the p-value from a hypothesis test can be more accurate and reliable, leading to better data-driven decision-making.

Featured Posts

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Join the Statology Community

Sign up to receive Statology's exclusive study resource: 100 practice problems with step-by-step solutions. Plus, get our latest insights, tutorials, and data analysis tips straight to your inbox!

By subscribing you accept Statology's Privacy Policy.