Fertility rates (children born per woman) are shown for 15 EU nations in 2 years a decade apart.

step 1 So if we look at this histogram here, it's beautiful indeed. But what we can see is that there's

Fertility rates (children born per woman) are shown for 15...

Fertility rates (children born per woman) are shown for $15 \mathrm{EU}$ nations in 2 years a decade apart. Research question: At $\alpha=.05$, is there a significant rank correlation? Note: Only the first 3 and last 3 nations are shown. $$ \begin{array}{lcc} \hline \text { Fertility Rates in EU Nations }(\boldsymbol{n = 1 5}) & \\ \hline \text { Nation } & \mathbf{1 9 9 0} & \mathbf{2 0 0 0} \\ \hline \text { Austria } & 1.5 & 1.3 \\ \text { Belgium } & 1.6 & 1.5 \\ \text { Denmark } & 1.6 & 1.7 \\ \quad \vdots & \vdots & \vdots \\ \text { Spain } & 1.4 & 1.1 \\ \text { Sweden } & 2.0 & 1.4 \\ \text { United Kingdom } & 1.8 & 1.7 \\ \hline \end{array} $$

Fertility rates (children born per woman) are shown for $15 \mathrm{EU}$ nations in 2 years a decade apart. Research question: At $\alpha=.05$, is there a significant rank correlation? Note: Only the first 3 and last 3 nations are shown.
$$
\begin{array}{lcc}
\hline \text { Fertility Rates in EU Nations }(\boldsymbol{n = 1 5}) & \\
\hline \text { Nation } & \mathbf{1 9 9 0} & \mathbf{2 0 0 0} \\
\hline \text { Austria } & 1.5 & 1.3 \\
\text { Belgium } & 1.6 & 1.5 \\
\text { Denmark } & 1.6 & 1.7 \\
\quad \vdots & \vdots & \vdots \\
\text { Spain } & 1.4 & 1.1 \\
\text { Sweden } & 2.0 & 1.4 \\
\text { United Kingdom } & 1.8 & 1.7 \\
\hline
\end{array}
$$

Key Concepts

Spearman’s Rank Correlation Coefficient

This is a common statistic used to measure rank correlation. It quantifies how well the relationship between two variables can be described using a monotonic function. A value close to +1 or -1 indicates a strong monotonic relationship, while a value near 0 suggests little to no association.

p-Value

The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, under the null hypothesis. In rank correlation analysis, if the p-value is less than the significance level, the null hypothesis is rejected, indicating a statistically significant correlation between the ranked variables.

Significance Level (?)

The significance level, often denoted by alpha (?), represents the threshold for determining whether a result is statistically significant. With ? = 0.05, there is a 5% risk of concluding that a significant rank correlation exists when it actually does not.

Rank Correlation

Rank correlation assesses the strength and direction of the relationship between two ranked variables. Unlike Pearson’s correlation, it does not require the assumption of normally distributed data and is based on the order of data rather than their numerical values, making it ideal for non-parametric analysis.

Hypothesis Testing

In the context of rank correlation, hypothesis testing involves setting up a null hypothesis that there is no correlation between the rankings of the two variables, and an alternative hypothesis that a correlation exists. The test then determines whether any observed correlation is statistically significant.

Transcript

Please give Ace some feedback