Interested in statistically significant data? Read on!

## Statistically Significant Data: Definition

Let's begin with a definition.

**Statistically significant data** refers to results of an experiment that are likely to be attributed to a specific cause.

If data from an experiment is statistically significant, the result is unlikely to have occurred by chance.

It's important to consider sampling error, probability, and certainty.

**Sampling error:**a statistical error that occurs when an analyst selects a sample that does not effectively represent the entire population.**Probability:**the likelihood of an event happening.

**Probability vs Certainty**

Nothing in life is 100% certain. You could grow wings and gain the ability to fly. Yes, it's highly unlikely – but not impossible. There's no way of knowing for sure.

So in statistics, we use probability, not certainty.

## Statistical Analysis and Statistically Significant Data

What are statistics, and why do we need them?

**Statistics **are tests used to analyse, interpret, and present numerical data.

Without statistical tests, our data doesn't really mean anything. It's just a collection of numbers. But by analysing our data, we can find** associations or differences** between our data, which back up our results and help us to understand the natural environment better.

### Hypotheses

When planning an experiment, scientists make two hypotheses – the null hypothesis and the alternative hypothesis.

The **null hypothesis (H _{0}) **states that there will be no significant relationships or differences in the data.

The** alternative hypothesis (H _{1})** states that there will be a significant relationship or difference in the data.

Amy wants to know if babies prefer playing with blue toys over orange toys.

H_{0}: Babies do not prefer playing with blue toys over orange toys.

H_{1}: Babies prefer playing with blue toys over orange toys.

If the experiment shows a statistically significant result, the null hypothesis will be **rejected**. If it doesn't show a statistically significant result, the null hypothesis will be **accepted**.

## Testing for Statistical Significance

To check that the results of a statistical test are significant, we need to check the significance level and the degrees of freedom.

### Significance Levels

The **significance level** (also called the p-value) is the probability of incorrectly rejecting the null hypothesis.

The p-value describes probability, not certainty.

In biology and environmental science, the significance level is **0.05**. That means that if there is a** less than 5% chance of incorrectly rejecting the null hypothesis**, the data is considered statistically significant.

### Degrees of Freedom

Degrees of freedom = **n – 1**, where n is the size of the data set.

Using degrees of freedom helps us find** critical cut-off values** for statistical tests. The more degrees of freedom there are, the larger the critical value.

Critical values are found in tables. You can easily find them online, or in a statistics book.

## Statistically Significant Data: Variance

Variance is a way of measuring the differences between two datasets. It considers **the spread of data points** within a dataset.

Scientists can test for variance using the **F-test**. How does it work?

Calculate the

**mean**of your data set.Subtract each data point from the mean to find its deviation.

**Square**each deviation to ensure you have a positive number.Find the

**sum**of the squares.Divide the squares by

**n-1**to find out the variances.**Divide**the larger variance by the smaller variance to find the calculated F-value.**Compare**the calculated value to the critical value. If the calculated value is less than the critical value, there is a statistically significant variance.

n is the size of your dataset.

### Variance: Example

A meteorologist wanted to see if there is a significant difference between the wind speed in Hull and the wind speed in Nottingham. She wrote two hypotheses.

**Null Hypothesis:**There is no significant difference between the wind speed in Hull and the wind speed in Nottingham.**Alternative Hypothesis:**There is a significant difference between the wind speed in Hull and the wind speed in Nottingham.

Then, she collected monthly averages and used them to calculate the variance.

Month | Hull: Wind Speed (kph) | Hull: Deviation | Hull: Deviation^{2} | Nottingham: Wind Speed (kph) | Nottingham: Deviation | Nottingham: Deviation^{2} |

January | 24.3 | -4.2 | 17.64 | 21.5 | -3.2 | 10.24 |

February | 23.0 | -2.9 | 8.41 | 20.7 | -2.4 | 5.76 |

March | 21.5 | -1.4 | 1.96 | 19.8 | -1.5 | 2.25 |

April | 18.9 | 1.2 | 1.44 | 17.6 | 0.7 | 0.39 |

May | 17.7 | 2.4 | 5.76 | 16.8 | 1.5 | 2.25 |

June | 16.3 | 3.8 | 14.44 | 15.7 | 2.6 | 6.76 |

July | 16.1 | 4.0 | 16 | 15.7 | 2.6 | 6.76 |

August | 17.1 | 3.0 | 9 | 16.0 | 2.3 | 5.29 |

September | 19.3 | 0.8 | 0.64 | 17.4 | 0.9 | 0.81 |

October | 21.4 | -1.3 | 1.69 | 18.8 | -0.5 | 0.25 |

November | 22.4 | -2.3 | 5.29 | 19.4 | -1.1 | 1.21 |

December | 23.3 | -3.2 | 10.24 | 20.4 | -2.1 | 4.41 |

Mean | 20.1 | N/A | N/A | 18.3 | N/A | N/A |

Sum | N/A | N/A | 92.51 | N/A | N/A | 46.38 |

For Hull, the mean wind speed is 20.1 kph. The sum of squared deviations is 92.51.

Variance:

92.51 ÷ (12-1)

92.51 ÷ 11 = 8.41

For Nottingham, the mean wind speed is 18.3 kph. The sum of squared deviations is 46.38.

Variance:

46.38 ÷ (12-1)

46.38 ÷ 11 = 4.22

Calculated F-value = 8.41 ÷ 4.22 = **1.99**

Finally, the meteorologist found the **critical f-value** from a table. She made sure to check the **degrees of freedom** (in this example, 11) and the **significance level **(0.05).

For this test, the critical F-value is 2.16.

As the calculated F-value is** less than** the critical F-value, **there is a statistically significant variance** between the datasets. The meteorologist** rejected** the null hypothesis.

## Statistically Significant Data: Correlation

Spearman's Rank Correlation Coefficient is used to test for an **association or relationship between two variables**. The relationship can be positive or negative.

**Positive relationship:**an increase in one variable is associated with an increase in the other**Negative relationship:**an increase in one variable is associated with a decrease in the other

When performing a Spearman's Rank test, it's important to understand that **correlation ≠ causation**. Just because two things are linked doesn't mean that one causes a change in the other.

Chocolate consumption per capita is correlated with Nobel Prizes per capita. Unfortunately, that doesn't necessarily mean that eating more chocolate makes you smarter!

How does Spearman's Rank work?

**Rank**the data points for both variables.Work out the

**difference**between the ranks.**Square**the difference in ranks to ensure that you have a positive number.**Substitute**your data into the equation shown below to find the calculated r-value.**Compare**the calculated value to the critical value. If the calculated value is equal to or above the critical value, there is a statistically significant variance.

When ranking data, it can be from smallest to largest or largest to smallest. Just make sure that you rank both variables using the same method.

**Equation:** p = 1 – (6 x ∑ D^{2}) ÷ (n(n^{2}-1))

- D: difference in ranks
- n: number of data points in the set

### Correlation: Example

A zoologist wanted to see if the number of spots on a Dalmatian was related to its weight. He wrote two hypotheses.

**Null Hypothesis:**The number of spots on a Dalmatian is not related to its weight.**Alternative Hypothesis:**The number of spots on a Dalmatian is related to its weight.

He weighed ten adult Dalmatians and counted how many spots they had.

Weight (kg) | Spots | Rank of Weight | Rank of Spots | Difference between Ranks | Difference^{2} |

24.8 | 113 | 6 | 5 | 1 | 1 |

22.2 | 144 | 3 | 8 | -5 | 25 |

19.3 | 199 | 1 | 10 | -9 | 81 |

28.9 | 65 | 9 | 2 | 7 | 49 |

26.0 | 129 | 7 | 7 | 0 | 0 |

20.1 | 78 | 2 | 3 | -1 | 1 |

31.2 | 145 | 10 | 9 | 1 | 1 |

23.5 | 50 | 4 | 1 | 3 | 9 |

24.5 | 123 | 5 | 6 | -1 | 1 |

26.7 | 110 | 8 | 4 | 4 | 16 |

Sum | 184 |

Then, the zoologist inserted the data into the equation.

p = 1 – (6 × 184) ÷ (12(12^{2}-1))

p = 1 – (1104 ÷ 1716)

Calculated p-value = **0.356**

Finally, the zoologist found the critical p-value. For this test, the critical p-value was **0.553**. As the calculated p-value was less than the critical p-value, **there is not a statistically significant correlation** between the variables. The zoologist **accepted** the null hypothesis.

I hope that this article has clarified statistically significant data for you. Statistically significant data is a result that is very unlikely to have occurred by chance. To determine if your data is statistically significant, you need to compare your calculated value to the critical value (which is dependent on the significance level and the degrees of freedom).

## Statistically Significant Data - Key takeaways

- Statistically
- We use statistical tests to find associations or differences in our data. This backs up our results and helps us to understand the natural world better.
- When planning an experiment, we write a null hypothesis and an alternative hypothesis. If the result is statistically significant, the null hypothesis is rejected.
- When testing for significance, we need to use significance levels (usually 0.05) and degrees of freedom (n-1).
- Variance measures the difference between two datasets, taking into consideration the spread of data points. An F-test is used to see if variance is statistically significant.
- A correlation tests for an association or relationship between two variables. A Spearman's Rank test is used to see if the correlation is statistically significant.

^{1. Aloys Leo Prinz}^{, Chocolate consumption and Noble laureates, }^{Social Sciences & Humanities Open}^{, 2020}

^{2. Harry Dean, Are Dalmatians Born With Spots: Most Don’t Know This, The Puppy Mag, 2022}

^{3. Hill’s, Dalmatian Dog Breed Information and Personality Traits, 2022}

^{4. Weather Spark, Climate and Average Weather Year Round in Hull, 2022}

^{5. Weather Spark, Climate and Average Weather Year Round in Nottingham, 2022}

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##### Frequently Asked Questions about Statistically Significant Data

What does statistically significant data mean?

Statistically significant data is a result that is very unlikely to have occurred by chance.

How do you know if data is statistically significant?

Once you have calculated the test value, compare it to the critical value. Its relation to the critical value will determine if your data is statistically significant.

How do you analyse statistical significance?

Statistically significant variance can be analysed using an F-test. Alternatively, a statistically significant correlation can be analysed using a Spearman's Rank test.

What is considered a statistically significant correlation?

If the calculated p-value is equal to or above the critical p-value, the correlation is considered to be statistically significant.

What standard deviation is statistically significant?

If the calculated p-value for standard deviation is less than the critical p-value, the standard deviation will be considered statistically significant.

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