# Minimum Detectable Effect (MDE)

### 1. What is Minimum Detectable Effect (MDE)?

It’s a minimum improvement over the conversion rate of the existing asset (baseline conversion rate) that you want the experiment to detect.

By setting MDE, you define the conversion rate increase sufficient for the system to declare the new asset winner. The lower MDE you set, the slighter conversion changes will be detected by the system. Basically, MDE measures the experiment sensitivity.

Highly sensitive settings, or low MDE, come along with a big sample size. The lower MDE, the more traffic you need to detect minor changes, hence the more money you have to spend on driving that traffic.

So, by configuring MDE you are flexible about connecting the experiment design with the costs you are ready to incur.

### 2. What’s the optimal MDE?

There’s no such thing as an ideal MDE, so SplitMetrics can’t recommend you the optimal value. This is a key custom parameter affecting your sample size and, by implication, the costs associated with the traffic. In other words, we suggest you defining MDE by yourself, taking into consideration your individual risks – money and time.

### 3. How does MDE affect my sample size?

MDE has a dramatic effect on the amount of traffic required to reach statistical significance. To know your maximum sample size, use the Evan Miller calculator for sequential A/B sampling. Make sure that your insert  relative value for MDE rather than absolute.

By setting smaller MDE, you tell the system to detect slighter conversion rate changes, which requires more traffic and possibly time. On the other hand, the larger MDE you set, the less traffic (and possibly time) is required to finish the test.

For example, to reach the significance level of 5%, you’ll require 2,922 total conversions with MDE = 10%. with MDE = 5% the sample size grows up to 11,141 total conversions.

Remember, however, that the sample size you see is only the maximum threshold required for a statistically significant result. Due to the nature of sequential A/B testing, the system will constantly check the difference between conversion rates of variations under testing. Once the difference is found, the test is finished and there’s no need to score the entire sample size.

### 4. How to calculate my MDE?

Although our system can count MDE for you, we strongly recommend setting it by yourself.  This parameter depends on your own risks – money you’re ready to allocate for the traffic acquisition and time you can wait for the experiment to run.

To get MDE that works for you, you have to understand:

• Traffic acquisition costs, or the money you invest in driving the required sample size;
• Potential revenue generated from ASO-acquired users, in other words, the money you can make from using the new asset with a higher conversion rate.

The best possible MDE implies that the potential revenue exceeds or compensates for the traffic acquisition costs.

## MDE calculation workflow

#### Step 1. Estimate the desired conversion rate lift

Let’s say the conversion rate of your product page with the existing icon is 20% (baseline conversion rate). You assume that the new icon should have at least a 22% conversion rate for you to use it instead of the existing icon.

So, you have to configure an experiment in such a way that it declares the winner when the conversion rate difference is at least 22% – 20% = 2%. To set that up, you have to count your estimated MDE.

MDE is calculated as a percent of the baseline conversion rate:

MDE = desired conversion rate lift / baseline conversion rate x 100%

In this example, 2% of the 20% baseline conversion rate is 10% – this is your estimated MDE for the experiment.

#### Step 2.  Calculate your sample size

Next step is to get your sample size, using the Evan Miller’s calculator for sequential A/B testing.

• Sample size calculation for experiments with two variations (A+B). Here’s what you should insert in the calculator:
1. Your estimated Minimum Detectable Effect: 10% (in this example). Important! Make sure that you use relative MDE.
2. Insert any value in the “Baseline conversion rate” field. As we use relative MDE, the baseline conversion rate is ignored in the sample size calculation;
3. Statistical power: 80% (default in SplitMetrics);
4. Significance level: 5% (default in SplitMetrics).

You will see the following:

Control wins if: 2,922 total conversions – this is the maximum sample size per two variations (A+B) needed to finish the experiment.

Treatment wins: 106 conversions ahead – means that the system will sequentially check the difference in conversions between variation A (control) and B, and may finish the experiment once the difference of 106 is found, even before reaching the maximum sample size.

• Sample size calculation for experiments with multiple variations (A+B+C+…)
1. Here’s what you should insert in the calculator:
1. Estimated MDE;
2. Any value as the baseline conversion rate;
3. Statistical power: 80%;
4. Significance level: when more than two variations are tested, you have to apply the Sidak correction to the significance level.

Why? Each pair of variations has its individual significance level. As the number of variations under testing grows, so does the overall significance level because those individual values accumulate. The Sidak correction balances out individual significance levels so that the overall significance level equals 5%.

To apply the Sidak correction, use the following significant level values:

 Number of variations under testing (incl. control) Significance level to set 3 (A+B+C) 3% 4 (A+B+C+D) 2% 5 (A+B+C+D+E) 1%
1. Get the total conversions.

The total conversions will appear after you insert all the above in the calculator.

For example, you want to run an experiment with 3 variations – A+B+C. Things you’ll insert in the calculator will be:

1. Estimated MDE: 10% (can be another value, depending on the conversion rate lift you want the system to detect);
2. Statistical power: 80%
3. Significance level: 3%

Total conversions required: 3,472

1. Divide the total conversions by 2.

In the above example with 3 variations, you’ll get:

total conversions / 2 = 3,472 / 2 = 1,736

1. Multiply the result received in step 3 by the number of variations, including control:
• For A+B+C: total conversions / 2 * 3
• For A+B+C+D: total conversions / 2 * 4
• For A+B+C+D+E:  total conversions / 2 * 5

Back to the example, as you run an A+B+C experiment, 3 will be your multiplier:

total conversions / 2 * 3 = 5,208

5,208 is the rough estimation of the maximum sample size for an experiment with 3 variations (A+B+C).

#### Step 3. Calculate your traffic acquisition costs

In step 2, we’ve calculated the maximum required conversions for an experiment with two variations (A+B) – 2,922. Now that you know the maximum required sample size, you can calculate the possible traffic acquisition costs. Use this formula:

traffic acquisition costs = total conversions / baseline conversion rate *  Сost per Сlick

Note: By dividing the total conversions by your baseline conversion rate you gauge your sample size in visitors (those who click on your ad banner).

Let’s say your Сost per Сlick is \$0.5 and the baseline conversion rate is 20% (convert it to the decimal form to use in the formula). Your traffic acquisition costs will be:

2,922 / 0.2 * \$0.5 = \$7,305

When you have SplitMetrics integrated with Facebook Pixel, you may configure “Complete Registration” as a conversion event. In such a case, the traffic acquisition costs will be calculated considering users who click on the “Get” button rather than those who click on an ad banner.

The formula for cost calculations in such cases will include Cost per Install (not Сost per Сlick):

traffic acquisition costs = total conversions x CPI

Note: As you can see, you don’t have to recalculate sample size in visitors. Just multiply CPI by the total conversions obtained in the Evan Miller calculator.

Let’s say your Cost per Install is \$2.5 and the maximum sample size is 2,922 total conversions. Your traffic acquisition costs will be:

2,922 X \$2.5 = \$7,305

At this point, you have to make sure that these costs line up with the budget allocated for the traffic acquisition:

• If no, set a bigger MDE, which will require a smaller sample size, hence smaller acquisition costs; however, if your variations are quite similar, a big value for MDE won’t be able to deliver a result.
• If yes, proceed with calculating the potential revenue generated from ASO-acquired users.

#### Step 4.  Calculate the potential revenue

You may use different ways to calculate the potential revenue from the conversion rate lift, for example, based on the LTV of ASO-acquired app subscribers. In the above described example with two variations (A+B), you have to calculate how much money you will generate from a 2% conversion rate lift.

Once you have your Potential revenue (\$Y) calculated, compare it with the Traffic acquisition costs (\$X):

• if the potential revenue is greater than the traffic acquisition costs (\$Y > \$X), you can go with the estimated MDE in your experiment;
• if the traffic acquisition costs exceed the potential revenue (\$Y < \$X), estimate a bigger MDE and repeat all the steps above.

### 5. At what experiment stage should I set MDE?

MDE is configured after the experiment is created but before you start driving traffic. If you change your MDE after the traffic starts driving to the experiment, you will lose all the statistics.

### 6. Can I change my MDE during the experiment?

Don’t modify MDE after you start driving traffic to your experiment. Otherwise, all the statistics – visitors, conversions, improvement, etc. – will be reset.

### 7. How does SplitMetrics calculate my MDE?

To arrive at your best possible MDE, our algorithm will rely on your baseline conversion. Your ideal MDE will be the value which produces a sufficiently large sample size, yet comparable to that in classic A/B testing.

If SplitMetrics calculates MDE for you, be aware that the result won’t appear straight away. The algorithm will gauge and  display your MDE in the interface after your variations gain enough conversions.