# Banner Test - Banner Message Compare

For additional documentation on the testing methodology please see the following pages:

## Banners

#### Result

Test Time: 2010-12-23 19:00:00 UTC - 2010-12-24 01:00:00 UTC
Sampling Interval = 10 minutes
Testing Interval = 360 minutes
Total Number of Samples per Class = 36

TEST RESULT INCONCLUSIVE

(*) The rate of donations per banner impression over a fixed time interval.

(**) The rate of amount50 per banner impression over a fixed time interval. Amount50 is the dollar amount raised from donations initiated under a given banner where all donations of more than \$50 are recorded as \$50 donations. This counters the skewing effect of outlier donations.

## Data Analysis

This section analyzes and interprets the results of the tests. It should be noted that the data is analyzed over a period at least as large as the full testing period and that the testing period was chosen based on the period of time where significant hits and donations were observed.

### Data Consistency and Cleaning

The plots below display the counts of the data sources over the testing period as verification of the consistency of the donation pipeline data used in testing. It should be noted that a certain amount of natural variance is expected in donation counts and is no cause for alarm. The bottom two figures depict the total views and donations with those coming from each banner. This illustrates when the campaign becomes active and is also a useful tool for determining where anomalous behaviour may be visible in the data.

Analyzing the above plots the donation and impression data appear to be quite regular over the interval 2010-12-23 19:00:00 UTC - 2010-12-24 01:00:00 UTC. Therefore, ten minute intervals will be used for sampling over this period as a source for the paired t-test to assess confidence in the winner.

### Modelling and Hypothesis Testing

"Urgent Appeal" won in each case for donations/impression and amount50/impression with increases of 5.74% and 5.20% respectively. The student's t-test was used to assess confidence over each metric and the confidence in the winner for donations/impression and amount50/impression is at least 75.0% and 60.0% respectively. This is a very slight and non-significant win for the "Urgent Appeal". Both banners effectively performed the same.

```
TOTAL DONATIONS "Urgent Appeal": 399
TOTAL DONATIONS "You learned a lot this year": 378

TOTAL AMOUNT50* RAISED "Urgent Appeal": \$10419.00
TOTAL AMOUNT50* RAISED "You learned a lot this year": \$9873.88

* AMOUNT50 indicates the total amount raised where all donations greater than \$50 are taken to be a donation of \$50.

```
```
DONATIONS PER IMPRESSION:

Between 75.0% and 90.0% confident about the winner.

Banner message Compare -- 2010-12-23 19:00:00 - 2010-12-24 01:00:00

item 1  = "You learned a lot this year"
item 2  = Urgent appeal

The winner Urgent appeal had a 5.74% increase.

interval	mean1		mean2		stddev1		stddev2

0		0.00008		0.00009		0.00000		0.00005
1		0.00008		0.00009		0.00002		0.00002

Overall Parameters:

mean1		mean2		stddev1		stddev2
0.00008		0.00009		0.00001		0.00004

```
```
AMOUNT50 PER IMPRESSION:

Between 60.0% and 75.0% confident about the winner.

Banner message Compare -- 2010-12-23 19:00:00 - 2010-12-24 01:00:00

item 1  = "You learned a lot this year"
item 2  = Urgent appeal

The winner Urgent appeal had a 5.20% increase.

interval	mean1		mean2		stddev1		stddev2

0		0.00208		0.00218		0.00004		0.00092
1		0.00217		0.00229		0.00108		0.00025

Overall Parameters:

mean1		mean2		stddev1		stddev2
0.00212		0.00223		0.00077		0.00067

```

## Endnotes

1. Campaign = "20101223JA056"
2. "Urgent appeal" utm_source = "20101223_JA028A_US"
3. "You learned a lot this year"" utm_source = "20101223_JA028C_US"