{ "version": "https:\/\/jsonfeed.org\/version\/1.1", "title": "Ivan Baldin, Data Analyst: posts tagged A\/B test", "_rss_description": "Data analytics, probability theory, and applied statistics — from the practitioner’s perspective. Ivan Baldin writes about sales funnels, call center performance, conversion analysis, confidence intervals, binomial distributions, Z-scores, and the math behind data-driven decisions. Years of hands-on experience turning raw CRM data into actionable insights for sales teams and business leaders.", "_rss_language": "en", "_itunes_email": "", "_itunes_categories_xml": "", "_itunes_image": "", "_itunes_explicit": "", "home_page_url": "https:\/\/ivanbaldin.blog\/tags\/a-b-test\/", "feed_url": "https:\/\/ivanbaldin.blog\/tags\/a-b-test\/json\/", "icon": "https:\/\/ivanbaldin.blog\/pictures\/userpic\/userpic@2x.jpg?1774085044", "authors": [ { "name": "Ivan Baldin", "url": "https:\/\/ivanbaldin.blog\/", "avatar": "https:\/\/ivanbaldin.blog\/pictures\/userpic\/userpic@2x.jpg?1774085044" } ], "items": [ { "id": "5", "url": "https:\/\/ivanbaldin.blog\/all\/kupivip-voice-bot-guessing-the-sample-size\/", "title": "KupiVIP’s Voice Robot: Guessing the Sample Size", "content_html": "

In the article “Case Study: On Black Friday, KupiVIP Replaced Their Call Center with a Robot, and Only 5 Out of 5,000 People Realized They Were Talking to a Neural Network<\/a>” on vc.ru, one phrase caught my attention above all else — the part where the author mentions a conversion rate increase from 6% to 8%:<\/p>\n

\n\""the\n<\/div>\n

Naturally, I started wondering: on what call volume was this conversion rate increase observed, and was that volume sufficient to make a reliable claim that the voice robot outperforms live call center agents?<\/p>\n

The question can be formulated precisely as follows: what is the minimum number of calls required to claim, with a confidence level of, say, 95%, that the conversion rate “increased from 6% to 8%”?<\/p>\n

Building the Experiment in Google Spreadsheets<\/h2>\n

Let’s lay out the available data in Google Spreadsheets. For the calculations that follow, we’ll need a “number of calls” parameter — let’s assume for now that both the robot and live agents each made 1,000 calls before the 6% and 8% conversion rates were obtained:<\/p>\n

\n\"\"\n<\/div>\n

Essentially, this is a standard A\/B split test, and we’ll need to walk through its algorithm to obtain the Z-score<\/i> and calculate the p-value<\/i>.<\/p>\n

Let’s calculate the standard errors (SD, or σ) for both conversion rates, along with the standard error of the difference between them. The formula for the standard error of a conversion rate:<\/p>\n

\n\"\"\n<\/div>\n

where p<\/i> is the conversion rate (6%, for example) and n<\/i> is the sample size (1,000 calls). Here’s the Google Spreadsheets calculation:<\/p>\n

\n\"\"\n<\/div>\n

The standard error of the difference between conversion rates is calculated using the formula:<\/p>\n

\n\"\"\n<\/div>\n

where σ<\/i> is the standard error of each conversion rate, A and B (live agent and robot). We’ll compute it just below in Google Spreadsheets:<\/p>\n

\n\"\"\n<\/div>\n

How much larger is the difference between conversions A and B compared to the standard error of that difference? This ratio is called the Z-score.<\/i><\/b> In Google Spreadsheets, it’s straightforward:<\/p>\n

\n\"\"\n<\/div>\n

So the Z-score = 1.7541. On the normal distribution curve, this corresponds to the 96th percentile — meaning the probability of the Z-score randomly exceeding 1.7541 is about 4% (in other words, 96% of the area under the bell curve falls within +1.7541 standard deviations):<\/p>\n

\n\"\"\n<\/div>\n

Where did we get 96%? The exact probability, the p-value<\/i>, is calculated using the formula:<\/p>\n

=NORM.DIST(1.7541,0,1,TRUE)<\/code><\/pre>
\n\"\"\n<\/div>\n
P-value = 96.03%.<\/p>\n
So here’s our interim conclusion: if, on a sample of 1,000 calls in each of the two groups, we observed conversion rates (promo code activations) of 6% and 8%, then we are 96% confident that this difference is not due to chance.<\/b> (There remains a 4% probability that the observed difference is random. In that case, perhaps the conversion rate is actually the same — say, 7% — and had we made more calls, the difference would have eventually disappeared.)<\/p>\n
Minimum Experiment Size<\/h2>\n
Now, let’s get back to the original question.<\/p>\n
We weren’t trying to prove that 8% is greater than 6%, and the figure of 1,000 calls for the robot and agents was chosen arbitrarily. What we wanted to calculate was the minimum number of calls needed to establish the statistical significance of the difference between 8% and 6% at a 95% confidence level.<\/b><\/p>\n
1,000 calls turned out to be more than enough. Now we just need to decrease this number until the p-value crosses the 95% threshold. (By the way, according to the normal distribution formula, this corresponds to a Z-score of 1.6449 — try verifying this yourself.)<\/p>\n
In theory, it would probably be possible to derive a large formula for the n<\/i> at which the p-value equals 0.95. In practice, it’s faster to manually find the minimum n through trial and error. Or, better yet, install a Goal Seek<\/b> add-on for Google Spreadsheets and use it to find the answer automatically:<\/p>\n
\n\"\"\n
(Just make sure the number of robot calls is exactly the same as the number of live agent calls, i.e., you’ve entered =C6 in cell C7.)<\/div>\n<\/div>\n
\n\"\"\n<\/div>\n
Conclusions<\/h2>\n
So, we’ve calculated the minimum experiment conditions for evaluating the effectiveness of the KupiVIP voice robot.<\/p>\n
You need at least 879 calls<\/b> in each of the two groups to confirm, with a 95% confidence level, that there is a difference between the 6% promo code activation rate in the control group (real live agents) and the 8% rate in the test group (voice robot).<\/p>\n
(The only caveat is that neither 6% nor 8% yields a whole number of activations on a sample of 879 calls, and in reality, of course, the numbers would be different — and the number of calls in the two groups could vary as well. But this doesn’t really matter much, since the conversion rates cited in the article were most likely rounded.)<\/p>\n
See also:<\/h2>\n
https:\/\/abtestguide.com\/calc\/?ua=1000&ub=1000&ca=60&cb=80<\/a><\/p>\n",
            "summary": "A voice robot beats call center with 8% vs. 6% promo code activations. But how many calls do you actually need to prove the difference is real? We walk through the A\/B test math and find the minimum sample size for 95% confidence using Goal Seek in Google Spreadsheets, Z-score and SD.",
            "date_published": "2019-07-20T13:18:00+03:00",
            "date_modified": "2026-04-12T03:31:13+03:00",
            "tags": [
                "A\/B test",
                "call center",
                "conversion",
                "Google Sheets",
                "statistics"
            ],
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            "id": "7",
            "url": "https:\/\/ivanbaldin.blog\/all\/call-quality-audits-determining-your-sample-size\/",
            "title": "Call Quality Audits: Determining Your Sample Size",
            "content_html": "
Calculating Sample Size for Quality Call Audits<\/h2>\n
A common tool for assessing the quality of sales managers’ work is quality auditing of phone calls<\/b>, or “call monitoring.”<\/p>\n
Suppose your goal is not simply to measure<\/b> the quality of phone calls, but to document growth<\/i> in that quality.<\/b> For example, you conducted training for your managers, introduced new incentives for meeting quality standards, or implemented some other intervention.<\/p>\n
\n\"\"\n<\/div>\n
It’s reasonable to assume that an improvement in quality in the first random call recorded after the training won’t definitively prove that quality has improved across all calls. Likely, a second successful call won’t conclusively confirm the hypothesis either.<\/p>\n
Thus, you’ll need to listen to — if not all calls — at least a sufficient number<\/b> of calls after your changes, and the number of calls you’ll need to audit can, in fact, be calculated precisely.<\/b><\/p>\n
Calculating Sample Size<\/h2>\n
On page 35 of the paper “Introduction to Statistical Inference and Experimental Design<\/a>” I found a suitable example 1.9 and a formula for calculating such samples:<\/p>\n
\n\"\"\n<\/div>\n
In this example, an improvement in ACT<\/a> math test scores from 24.5 (variance 8.2) to 26.0 points is considered, with α = 0.05 and power = 0.90.<\/p>\n
For convenience, I assembled the formula in a Google Sheet:<\/p>\n
Sample Size Calculator<\/a><\/p>\n
\n\"\"\n
You simply need to copy the file and substitute your own values.
\nIt’s reasonable to choose a confidence level between 80% and 95%, and a statistical power between 60% and 80%. Enter the average call quality score before changes, the standard deviation (SD) of call scores “before,” and the expected average call quality score “after” your changes.<\/div>\n<\/div>\n
See also:<\/h2>\n
https:\/\/bpb-us-e1.wpmucdn.com\/sites.ucsc.edu\/dist\/2\/1389\/files\/2026\/03\/part1.pdf<\/a><\/p>\n",
            "summary": "Stop guessing how many calls to audit. Use this statistical formula to calculate the exact sample size needed for call audits that prove quality improvements. Learn about confidence levels, power calculations, and A\/B testing verification for your sales team.",
            "date_published": "2019-05-26T16:46:00+03:00",
            "date_modified": "2026-04-18T14:21:49+03:00",
            "tags": [
                "A\/B test",
                "call center",
                "equations",
                "Google Sheets",
                "Sales Department"
            ],
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            "_date_published_rfc2822": "Sun, 26 May 2019 16:46:00 +0300",
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