# Using the Hypothesis

Test in Excel To Test

Headlines

This article will show exactly how to perform a Hypothesis Test in Excel to test whether one headline performs better than another headline in a pay-per-click Internet marketing campaign. This Hypothesis Test will be testing the Null Hypothesis that both headlines perform at the same level.

Specifically, we will show how to use Excel to perform a One-Tailed test, a Two-Sample test , Unpaired, Hypothesis Test of Proportion to determine whether Headline 2 converts better than Headline 1 when used in the same PPC ad. Different types of Hypothesis Tests such as a Paired test, a Two-tailed test, and a Hypothesis Test of Mean are demonstrated in other articles of this blog.

The advantages of statistical analysis in Excel to solve business statistics problems is that most problems can be solved in just one or two steps and there is no more need to look anything up on Normal Distribution tables.

Here is the problem:

**Problem: An Internet marketing manager is testing the effectiveness of two different headlines when used in the same pay-per-click ad. The Internet marketing manager is trying to determine whether Headline 2 is better than Headline 1. Headline 1 was inserted into a PPC ad. Running this Headline 1/ad combination resulted in 80 click-throughs. 52 of those 80 click-through visitors converted (purchased).**

**Headline 2 was run with the same PPC ad under the same conditions and approximately the same number of ad impressions. Running this combination of Headline 2/ad resulted in 90 click-throughs, of which 63 converted. Determine within an error of 1% whether Headline 2 converted better than Headline 1.**

Here are the Conversion Data for Headlines 1 and 2:

**Headline 1**

p

**1avg**= Sample proportion 1 = 52 / 80 = 0.65 converted

q

**1avg**= 1 - p

**1avg**= 1 - 0.65 = 0.35 not converted

n

**1**= Sample size 1 = 80

**Headline 2**

p

**2avg**= Sample proportion 2 = 63 / 90 = 0.70 converted

q

**2avg**= 1 - p

**2avg**= 1 - 0.70 = 0.30 not cconverted

n

**2**= Sample size 2 = 90

α = 0.01 = alpha = Level of significance, therefore there is a 1% max chance of error.

This results in a 99% Level of Certainty Required

Before we begin solving this problem, we need to know whether we are dealing with normally distributed data. If the data is not normally distributed, we have to use nonparametric statistical tests to solve this problem.

**Always Test for Normality First**

Normality tests should be performed on both Headline 1 and Headline 2 conversion data. Both data sets must be normally distributed to perform the well-known hypothesis test that is based upon the underlying data being normally distributed. This blog has numerous articles about how to perform normality testing and nonparametric testing if the data is not normally distributed.

__The MOST Important Step__

Determine What Type of Hypothesis

Determine What Type of Hypothesis

Test You Will Perform

Test You Will Perform

**1) Hypothesis Test of Mean or Proportion?**

We know that this is a

**test of proportion**and not mean because

**because each individual sample taken has only 2 possible values: the headline/ad combination either converted the click-through visitor or it didn't.**

**2) One or Two-Tailed Hypothesis Test?**

We know that this is a

**one-tailed test**because we are trying to

**determine if Headline 2 has a higher conversion rate than Headline 1**, not whether conversion rates are merely different, which would be a two-tailed test.

**3) One or Two-Sample Hypothesis Test?**

We know that

**two samples**must to be taken because no data is initially available.

**4) Paired or Unpaired Hypothesis Test?**

This is

**unpaired data**because groups are sampled independently. Hypothesis tests of proportion cannot be applied to paired data.

In this case, we are performing a

**to determine whether Headline 2 has a higher conversion rate than Headline 1. We will do this test in Excel. It is extremely important to establish the type of Hypothesis test.**

__One-Tailed, Two-Sample, Unpaired Hypothesis Test of Proportion__Each type of Hypothesis test uses a slightly (or very) different methodology and set of formulas. The previous 2 articles in this blog with provide examples of Hypothesis Tests of Mean. You will notice that the formulas for Mean Hypothesis Tests are completely different, but the 4-step method always works for any type of Hypothesis Test.

**The Four-Step Method That Solves**

__ALL__Hypothesis Tests**Step 1 - Create the Null and Alternate Hypotheses**

**1avg**and p

**2avg**, conversion rates from each headline are the same, then p

**1avg**- p

**2avg**= 0.

The Null Hypothesis states that both headlines the same conversion rates, which is equivalent to:

Null Hypothesis = H0 = p

**1avg**- p

**2avg**= 0

The Alternate Hypothesis states that Headline 2 is better than Headline 1, which is equivalent to:

The Alternate Hypothesis, which states that p

**2avg**is greater than p

**1avg**, is as follows:

Alternate Hypothesis, H1 = p

**1avg**- p

**2avg**is less than 0

****************************

For this one-tailed test, the Alternative Hypothesis states that if the value of the distributed variable (p

**1avg**- p

**2avg**) is less than the value stated by the Null Hypothesis, the Region of Uncertainty will be in the outer left tail.

Note - the Alternative Hypothesis determines whether the Hypothesis test is a one-tailed test or a two-tailed test as follows:

One-tailed test - (Value of variable) is greater than OR is less than (Constant)

Two-tailed test - (Value of variable) does not equal (Constant)

**Step 2 - Map the Normal Curve**

We now create a Normal curve showing a distribution of the same variable that is used by the Null Hypothesis, which is (p

**1avg**- p

**2avg**). The mean of this Normal curve will occur at the same value of the distributed variable as stated in the Null Hypothesis.

Since the Null Hypothesis states that p

**1avg**- p

**2avg**= 0, the Normal curve will map the distribution of the variable (p

**1avg**- p

**2avg**) with a mean of (p

**1avg**- p

**2avg**) = 0

This Normal curve will have a standard error that is calculated as the standard error of a sampled proportion is normally calculated, as follows:

The standard error of the difference of proportions is:

s

**p1avg-p2avg**=

= SQRT [ p

**weighted*** q

**weighted**( 1 / n1 + 1 / n2 ) ]

p

**weighted**= (n1*p

**1avg**+ n2*p

**2avg**) / (n1 + n2)

= (n1*p

**1avg**+ n2*p

**2avg**) / (n1 + n2)

= [ (80 * 0.65) + (90 * 0.70) / (80 + 90) ]

= 0.676

q

**weighted**= 1 - p

**weighted**

= 1 - p

**weighted**

= 1 - 0.676

= 0.324

Standard Error = s

**p1avg-p2avg**=

= SQRT [ p

**weighted*** q

**weighted**( 1 / n1 + 1 / n2 ) ]

= SQRT [ ( 0.676 * 0.324 ) * ( 1 / 80 + 1 / 90 ) ]

= 0.0719

*Click On Image To See Larger Version*The problem requires a 99% Level of Certainty so the Region of Certainty will contain 99% of the area under the Normal curve.

We know that this problem uses a one-tailed test with the Region of Uncertainty entirely contained in the outer left tail.

The Region of Uncertainty contains 1% of the total area under the Normal curve. The entire 99% Region of Certainty lies to the right of the 1% Region of Uncertainty, which is entirely contained in the outer left tail.

****************************************

We need to find out how far the boundary of the Region of Certainty is from the Normal curve mean. Calculating the number of standard errors from the Normal curve mean to the outer boundary of the Region of Certainty in the right tail for a one-tailed test is done as follows:

z

**99%**,

**1-tailed**= NORMSINV(1 - α) = NORMSINV(

**0.99**) = 2.33

*Excel Note - NORMSINV(x) = The number of standard errors from the Normal curve mean to a point right of the Normal curve mean at which x percent of the area under the Normal curve will be to the left of that point.*

*Additional note - For a one-tailed test, NORMSINV(x) can be used to calculate the number of standard errors from the Normal curve mean to the boundary of the Region of Certainty whether it is in the left or the right tail.*The Region of Certainty extends to the left of the Normal curve mean of (p1avg - p2avg) = 0 by 2.33 standard errors.

One standard error = s

**p1avg-p2avg**= 0.0719, so:

2.33 standard errors = (2.33) * (0.0719) = 0.1675

The outer left boundary of the Region of Certainty has the value

= µ - z

**99%,1-tailed*** s(

**p1avg-p2avg**)

which equals 0 - (2.33) * (0.0719) = - 0.1675

This point (-0.1675) is 2.33 standard errors to the left of the Normal curve mean of (p

**1avg**- p

**2avg**) = 0

This point (-0.1675) is the left boundary of the 99% Region of Certainty on the Normal curve.

*Click Image To See Larger Version***Step 4 - Perform Critical Value and p-Value Tests**

**a) Critical Value Test**

The Critical Value Test is the final test to determine whether to reject or not reject the Null Hypothesis. The p Value Test, described below, is an equivalent alternative to the Critical Value Test.

The Critical Value test tells whether the value of the actual variable, p

**1avg**- p

**2avg**, falls inside or outside of the Critical Value, which is the boundary between the Region of Certainty and the Region of Uncertainty.

If the actual value of the distributed variable, p

**1avg**- p

**2avg**, falls within the Region of Certainty, the Null Hypothesis is not rejected.

If the actual value of the distributed variable, p

**1avg**- p

**2avg**, falls outside of the Region of Certainty and, therefore, into the Region of Uncertainty, the Null Hypothesis is rejected and the Alternate Hypothesis is accepted.

In this case, the actual value of the variable, p

**1avg**- p

**2avg**=

= 0.65 - 070 = -0.05

The actual value of the variable (p

**1avg**- p

**2avg**) = -0.05 and is therefore inside the Critical Value (-0.1675), which is the boundary between the Regions of Certainty and Uncertainty.

The actual value of the variable (p

**1avg**- p

**2avg**) is inside the Region of Certainty and therefore inside the Critical Value.

We therefore do not reject the Null Hypothesis and state that the Null Hypothesis is not disproven that both headlines have the same conversion rates..

*Click On Image To See Larger Version*

b) p Value Test

b) p Value Test

**1avg**- p

**2avg**).

p Value(

**p1avg-p2avg**) =

= NORMSDIST( [ (p

**1avg**- p

**2avg**) - µ ] / s(

**p1avg - p2avg**) )

**************************************

*Excel note - NORMSDIST(x) calculates the total area under the Normal curve to the LEFT of the point that is x standard errors to the right of the Normal curve mean. If we are calculating the area to the RIGHT of this point, we would use 1 - NORMSDIST. This would be as follows:*p Value(

**p1avg-p2avg**) =

= 1 - NORMSDIST( [ (p

**1avg**- p

**2avg**) - µ ] / s(

**p1avg - p2avg**) )

******************************************************

Since we are calculating the area to the left of this point, we use:

p Value(

**p1avg-p2avg**) =

= NORMSDIST( [ (p

**1avg**- p

**2avg**) - µ ] / s(

**p1avg - p2avg**) )

= NORMSDIST((-0.05 - 0 ) / 0.0719) = NORMSDIST(-0.05/0.0719) = 0.24

The p Value (0.24) is greater than α (0.01), so the Null Hypothesis is not rejected.

For a one-tailed test- When the p Value is greater than α, the actual value of the distributed variable falls inside the Region of Certainty and the Null Hypothesis is not rejected.

This is the case here.

*Click Image To See Larger Version*Using the Hypothesis Test in Excel to Find Which Headline Works Best In Your PPC Ads

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**Excel Master Series Blog Directory**

Statistical Topics and Articles In Each Topic

- Histograms in Excel
- Bar Chart in Excel
- Combinations & Permutations in Excel
- Normal Distribution in Excel
- Overview of the Normal Distribution
- Normal Distribution’s PDF (Probability Density Function) in Excel 2010 and Excel 2013
- Normal Distribution’s CDF (Cumulative Distribution Function) in Excel 2010 and Excel 2013
- Solving Normal Distribution Problems in Excel 2010 and Excel 2013
- Overview of the Standard Normal Distribution in Excel 2010 and Excel 2013
- An Important Difference Between the t and Normal Distribution Graphs
- The Empirical Rule and Chebyshev’s Theorem in Excel – Calculating How Much Data Is a Certain Distance From the Mean
- Demonstrating the Central Limit Theorem In Excel 2010 and Excel 2013 In An Easy-To-Understand Way

- t-Distribution in Excel
- Binomial Distribution in Excel
- z-Tests in Excel
- t-Tests in Excel
- Overview of t-Tests: Hypothesis Tests that Use the t-Distribution
- 1-Sample t-Tests in Excel
- Overview of the 1-Sample t-Test in Excel 2010 and Excel 2013
- Excel Normality Testing For the 1-Sample t-Test in Excel 2010 and Excel 2013
- 1-Sample t-Test – Effect Size in Excel 2010 and Excel 2013
- 1-Sample t-Test Power With G*Power Utility
- Wilcoxon Signed-Rank Test As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013
- Sign Test As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013

- 2-Independent-Sample Pooled t-Tests in Excel
- Overview of 2-Independent-Sample Pooled t-Test in Excel 2010 and Excel 2013
- Excel Variance Tests: Levene’s, Brown-Forsythe, and F Test For 2-Sample Pooled t-Test in Excel 2010 and Excel 2013
- Excel Normality Tests Kolmogorov-Smirnov, Anderson-Darling, and Shapiro Wilk Tests For Two-Sample Pooled t-Test
- Two-Independent-Sample Pooled t-Test - All Excel Calculations
- 2-Sample Pooled t-Test – Effect Size in Excel 2010 and Excel 2013
- 2-Sample Pooled t-Test Power With G*Power Utility
- Mann-Whitney U Test in Excel as 2-Sample Pooled t-Test Nonparametric Alternative in Excel 2010 and Excel 2013
- 2-Sample Pooled t-Test = Single-Factor ANOVA With 2 Sample Groups

- 2-Independent-Sample Unpooled t-Tests in Excel
- 2-Independent-Sample Unpooled t-Test in Excel 2010 and Excel 2013
- Variance Tests: Levene’s Test, Brown-Forsythe Test, and F-Test in Excel For 2-Sample Unpooled t-Test
- Excel Normality Tests Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk For 2-Sample Unpooled t-Test
- 2-Sample Unpooled t-Test Excel Calculations, Formulas, and Tools
- Effect Size for a 2-Independent-Sample Unpooled t-Test in Excel 2010 and Excel 2013
- Test Power of a 2-Independent Sample Unpooled t-Test With G-Power Utility

- Paired (2-Sample Dependent) t-Tests in Excel
- Paired t-Test in Excel 2010 and Excel 2013
- Excel Normality Testing of Paired t-Test Data
- Paired t-Test Excel Calculations, Formulas, and Tools
- Paired t-Test – Effect Size in Excel 2010, and Excel 2013
- Paired t-Test – Test Power With G-Power Utility
- Wilcoxon Signed-Rank Test As a Paired t-Test Alternative
- Sign Test in Excel As A Paired t-Test Alternative

- Hypothesis Tests of Proportion in Excel
- Hypothesis Tests of Proportion Overview (Hypothesis Testing On Binomial Data)
- 1-Sample Hypothesis Test of Proportion in Excel 2010 and Excel 2013
- 2-Sample Pooled Hypothesis Test of Proportion in Excel 2010 and Excel 2013
- How To Build a Much More Useful Split-Tester in Excel Than Google's Website Optimizer

- Chi-Square Independence Tests in Excel
- Chi-Square Goodness-Of-Fit Tests in Excel
- F Tests in Excel
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- Pearson Correlation in Excel
- Spearman Correlation in Excel
- Confidence Intervals in Excel
- Overview of z-Based Confidence Intervals of a Population Mean in Excel 2010 and Excel 2013
- t-Based Confidence Intervals of a Population Mean in Excel 2010 and Excel 2013
- Minimum Sample Size to Limit the Size of a Confidence interval of a Population Mean
- Confidence Interval of Population Proportion in Excel 2010 and Excel 2013
- Min Sample Size of Confidence Interval of Proportion in Excel 2010 and Excel 2013

- Simple Linear Regression in Excel
- Overview of Simple Linear Regression in Excel 2010 and Excel 2013
- Simple Linear Regression Example in Excel 2010 and Excel 2013
- Residual Evaluation For Simple Regression in Excel 2010 and Excel 2013
- Residual Normality Tests in Excel – Kolmogorov-Smirnov Test, Anderson-Darling Test, and Shapiro-Wilk Test For Simple Linear Regression
- Evaluation of Simple Regression Output For Excel 2010 and Excel 2013
- All Calculations Performed By the Simple Regression Data Analysis Tool in Excel 2010 and Excel 2013
- Prediction Interval of Simple Regression in Excel 2010 and Excel 2013

- Multiple Linear Regression in Excel
- Basics of Multiple Regression in Excel 2010 and Excel 2013
- Multiple Linear Regression Example in Excel 2010 and Excel 2013
- Multiple Linear Regression’s Required Residual Assumptions
- Normality Testing of Residuals in Excel 2010 and Excel 2013
- Evaluating the Excel Output of Multiple Regression
- Estimating the Prediction Interval of Multiple Regression in Excel
- Regression - How To Do Conjoint Analysis Using Dummy Variable Regression in Excel

- Logistic Regression in Excel
- Logistic Regression Overview
- Logistic Regression Performed in Excel 2010 and Excel 2013
- R Square For Logistic Regression Overview
- Excel R Square Tests: Nagelkerke, Cox and Snell, and Log-Linear Ratio in Excel 2010 and Excel 2013
- Likelihood Ratio Is Better Than Wald Statistic To Determine if the Variable Coefficients Are Significant For Excel 2010 and Excel 2013
- Excel Classification Table: Logistic Regression’s Percentage Correct of Predicted Results in Excel 2010 and Excel 2013
- Hosmer-Lemeshow Test in Excel – Logistic Regression Goodness-of-Fit Test in Excel 2010 and Excel 2013

- Single-Factor ANOVA in Excel
- Overview of Single-Factor ANOVA
- Single-Factor ANOVA Example in Excel 2010 and Excel 2013
- Shapiro-Wilk Normality Test in Excel For Each Single-Factor ANOVA Sample Group
- Kruskal-Wallis Test Alternative For Single Factor ANOVA in Excel 2010 and Excel 2013
- Levene’s and Brown-Forsythe Tests in Excel For Single-Factor ANOVA Sample Group Variance Comparison
- Single-Factor ANOVA - All Excel Calculations
- Overview of Post-Hoc Testing For Single-Factor ANOVA
- Tukey-Kramer Post-Hoc Test in Excel For Single-Factor ANOVA
- Games-Howell Post-Hoc Test in Excel For Single-Factor ANOVA
- Overview of Effect Size For Single-Factor ANOVA
- ANOVA Effect Size Calculation Eta Squared (?2) in Excel 2010 and Excel 2013
- ANOVA Effect Size Calculation Psi (?) – RMSSE – in Excel 2010 and Excel 2013
- ANOVA Effect Size Calculation Omega Squared (?2) in Excel 2010 and Excel 2013
- Power of Single-Factor ANOVA Test Using Free Utility G*Power
- Welch’s ANOVA Test in Excel Substitute For Single-Factor ANOVA When Sample Variances Are Not Similar
- Brown-Forsythe F-Test in Excel Substitute For Single-Factor ANOVA When Sample Variances Are Not Similar

- Two-Factor ANOVA With Replication in Excel
- Two-Factor ANOVA With Replication in Excel 2010 and Excel 2013
- Variance Tests: Levene’s and Brown-Forsythe For 2-Factor ANOVA in Excel 2010 and Excel 2013
- Shapiro-Wilk Normality Test in Excel For 2-Factor ANOVA With Replication
- 2-Factor ANOVA With Replication Effect Size in Excel 2010 and Excel 2013
- Excel Post Hoc Tukey’s HSD Test For 2-Factor ANOVA With Replication
- 2-Factor ANOVA With Replication – Test Power With G-Power Utility
- Scheirer-Ray-Hare Test Alternative For 2-Factor ANOVA With Replication

- Two-Factor ANOVA Without Replication in Excel
- Creating Interactive Graphs of Statistical Distributions in Excel
- Interactive Statistical Distribution Graph in Excel 2010 and Excel 2013
- Interactive Graph of the Normal Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Chi-Square Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the t-Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Binomial Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Exponential Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Beta Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Gamma Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Poisson Distribution in Excel 2010 and Excel 2013

- Solving Problems With Other Distributions in Excel
- Solving Uniform Distribution Problems in Excel 2010 and Excel 2013
- Solving Multinomial Distribution Problems in Excel 2010 and Excel 2013
- Solving Exponential Distribution Problems in Excel 2010 and Excel 2013
- Solving Beta Distribution Problems in Excel 2010 and Excel 2013
- Solving Gamma Distribution Problems in Excel 2010 and Excel 2013
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