The results are telling you to “Fail to Reject the Null Hypothesis”.

Thus, even though the number of 5 defaults for Branch 1 and 9 defaults for Branch B seems to be a meaningful difference they aren’t different enough to support the Alternative Hypothesis.

Failing to Reject the Null Hypothesis with a Chi-Squared test for Independence and/or Proportions simply means the difference you are observing (e.g., in the default column) is just as likely to be a random chance as due to an assignable special cause.

Think of flipping 2 two-sided coins. The expectation (expected value) is equal distribution of heads and tails. Both coins could be “fairly” flipped (no trick coin and no gimmicks in the process. If each coin was flipped 100 times would you necessarily get an equal distribution of Heads and Tails..probably not. The coin toss wouldn’t be cited as having an assignable “Special Cause” driver until a specific threshold of improbability was met. When that improbability line is crossed the p-value will be less than the alpha value for the confidence level being tested at.

Therefore, if testing at 95% Confidence, the alpha value would be 0.05 (e.g., 5%). If the test Ch-Squared test result provided a p-value less than 0.05 (e.g., p=.001) then you would “Reject the Null Hypothesis”.

Rejecting the Null Hypothesis means your evidence from the test is strong enough to conclude the Alternative Hypothesis s more likely to be true. The difference in values CANNOT be explained away as random chance. The next step would be to investigate further and determine what Special Cause is driving a difference of Statistical Relevance (e.g., a “Rigged Coin” or a Gimmick in the process).

To learn more about this topic study how the “F” or Chi-Squared distribution Critical Value and respective Statistics are calculated. F Distribution and Chi-Squared Distribution analysis function the same way with the use of respective Degrees of Freedom tables to determine the Critical Value (the number of Rows and Columns determine the Critical Values in the table).

Meanwhile, an F or Chi-Squared “Statistic” is determined by the ratio of within variation (within subgroups) and between variations and is also impacted by the degrees of freedom. Reject the Null Hypothesis when the “Staistic” (e.g., F Statistic) is greater than the Critical Value (e.g., F Critical Value). Conversely, Fail to Reject the Null Hypothesis when the Statistic is less than the Critical Value.

NOTE: Magnitude matters. Susceptibility to a Type I Error (Producer’s Risk) or Type II Error (Consumer’s Risk) is greatest when the Test Statistic is close to the Critical Value. When this happens you should collect more data and run the test again.

Also, note that both the F Distribution and the Chi-Squared Distribution have the appearance of a long right-tailed Ski Slope. The distribution starts to look more normalized (approximating a flattened bell curve) when the number of degrees of freedom is substantially high (e.g., 20+ Degrees of Freedom).