In statistics, what is probable in one period of time may not be the same in another period. Likewise, what is probable in one set or group of data, may not be the same in another group.

To address this variability, we establish a certain level of confidence together with a margin of error (MOE). The margin of error is a small percentage value that is added and subtracted to/from the statistic to establish a range of values with a level of certainty. MOE is expressed with plus-minus (±).

The confidence level of 95%, which is used entirely on this blog, is standard in statistical analyses; however, a confidence level of 90% can also be used for smaller studies like using a sample size of about 750.

#### 95% Confidence Level and Margin Of Error

##### 2004 - 2008 Data

From 2004 to 2008, the EZ2 lotto draws happened once daily. Based on this period, the winning numbers are summarized in the preceding table showing how many times each number has won, with the corresponding margin of error (MOE) at 95% confidence or certainty level. The sample data consists of 1497 actual EZ2 lotto results.Lotto # | Frequency | Percent | ±MOE |
---|---|---|---|

Sum | 2994 | 100.0% | |

1 | 93 | 3.1 | 0.01 |

2 | 82 | 2.7 | 0.01 |

3 | 93 | 3.1 | 0.01 |

4 | 94 | 3.1 | 0.01 |

5 | 103 | 3.4 | 0.01 |

6 | 101 | 3.4 | 0.01 |

7 | 99 | 3.3 | 0.01 |

8 | 109 | 3.6 | 0.01 |

9 | 95 | 3.2 | 0.01 |

10 | 97 | 3.2 | 0.01 |

11 | 99 | 3.3 | 0.01 |

12 | 100 | 3.3 | 0.01 |

13 | 92 | 3.1 | 0.01 |

14 | 113 | 3.8 | 0.01 |

15 | 88 | 2.9 | 0.01 |

16 | 117 | 3.9 | 0.01 |

17 | 103 | 3.4 | 0.01 |

18 | 90 | 3.0 | 0.01 |

19 | 98 | 3.3 | 0.01 |

20 | 94 | 3.1 | 0.01 |

21 | 101 | 3.4 | 0.01 |

22 | 85 | 2.8 | 0.01 |

23 | 103 | 3.4 | 0.01 |

24 | 94 | 3.1 | 0.01 |

25 | 103 | 3.4 | 0.01 |

26 | 96 | 3.2 | 0.01 |

27 | 92 | 3.1 | 0.01 |

28 | 97 | 3.2 | 0.01 |

29 | 92 | 3.1 | 0.01 |

30 | 86 | 2.9 | 0.01 |

31 | 85 | 2.8 | 0.01 |

Based on the above data, notice that the percentage of winning of each number ranges from 2.74% to 3.77%, which is just around 3% for every number. This means that each number had a fair share of winning. Could the 3% probability be constant for every set of data? With MOE of ±1%, each number has the probability of winning at 2% - 4% (calculated as 3% ±1%). This can be true at 95% certainty or confidence level.