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Last updated on 2024年6月17日

How do you explain the difference between covariance and correlation to a non-statistician?

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When you dive into the world of statistics, two terms that often cause confusion are covariance and correlation. Both are measures that describe the relationship between two variables, but they do so in different ways. Imagine you're looking at the relationship between the time you spend studying and your exam scores. Covariance would tell you if there's a positive or negative relationship, meaning whether more study time is associated with higher scores or not. Correlation, on the other hand, quantifies that relationship, giving you an idea of how strong or weak it is. By the end of this article, you'll have a clearer understanding of these two concepts without needing a degree in statistics.

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Samadhan Ghubade

Senior Biostatistician II at ICON plc
Sweta Singh

IT Consultant & PPI Holder @ Infosys | MBA - IIMV'25 | Ex-Accenture
Osvaldo C.

1 Covariance Basics

Covariance is a measure that indicates the direction of the linear relationship between two variables. Think of it as a compass that shows whether the variables move together or in opposite directions. If you notice that as one variable increases, the other tends to increase as well, then the covariance is positive. Conversely, if one variable goes up and the other goes down, the covariance is negative. The tricky part is that covariance doesn't give you a standardized measure, so while it tells you the direction of the relationship, it doesn't tell you how strong it is.

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Samadhan Ghubade

Senior Biostatistician II at ICON plc
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Covariance is a measure of how two variables change together. If you notice that when one variable increases, the other tends to increase as well, they have a positive covariance. Conversely, if one variable increases while the other decreases, they have a negative covariance. When the variables do not show any consistent pattern of increasing or decreasing together. For instance, there might be no relationship between the number of hours you sleep and the number of emails you receive.

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Sweta Singh

IT Consultant & PPI Holder @ Infosys | MBA - IIMV'25 | Ex-Accenture
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Consider two stocks of Company A and Company B. Covariance measures how the returns of Company A's stock and Company B's stock move together. It's positive if they increase/decrease simultaneously, negative if they move oppositely. Correlation measures both direction and strength of the relationship between the returns of A's stock and B's stock and quantifies it on a scale from -1 to 1. When A’s stock goes up by a certain percentage, B’s stock goes up by the same percentage, they have a correlation of 1. When A’s stock goes up, & B’s stock goes down by the same percentage, and vice versa, they have a correlation of -1, and 0 if movements of one stock’s returns do not tell us anything about the movements of the other stock’s returns.

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Osvaldo C.
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La covarianza y la correlación son herramientas estadísticas para comprender y cuantificar las relaciones entre variables. Es esencial para la toma de decisiones informada, la predicción de tendencias y la optimización de estrategias en diversos campos. En el contexto multivariado, la covarianza se generaliza a una matriz de covarianza La covarianza : ??Relación direccional. ??Calculo de la correlación y la matriz covarianza. ??Análisis de riesgo por ejemplo como se mueven conjuntamente diferentes activos. ??Matriz covarianza. La correlación: ??Fuerza y dirección de la relación entre variables ( -1<normalizada<1 ?? Comparabilidad ??Modelos multivariados de predicción y análisis. ??Análisis multivariado :(PCA) y análisis factorial

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Cristiano Natal Tonéis

Professor Doutor (Educa??o Matemática) - Professor Gradua??o - Professor Universitário; Ensino e Pesquisa. Pós-Gradua??o. Postdoc.
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A covariancia é um cálculo usado para descobrir como funciona a rela??o entre dois tipos de dados.Se for nula, significa inexistência de rela??o entre os dados analisados; se for diferente de zero, aponta algum grau de dependência entre eles. Nulo: se o resultado for igual a zero, é sinal de que as variantes analisadas n?o impactam uma à outra; Positivo: se o resultado for um número positivo, significa que um ativo acompanha a subida e a queda do outro – ambos seguem a mesma dire??o; Negativo: quando o resultado é um número negativo, se conclui que um ativo tende a cair quando o outro sobe – os ativos seguem dire??es opostas.

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2 Correlation Defined

Correlation takes the concept of covariance one step further. It not only tells you the direction of the relationship between two variables but also quantifies its strength on a standardized scale from -1 to 1. A correlation of 1 means there's a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 implies no relationship at all. This makes correlation a more informative statistic than covariance because it provides context by telling you how closely two variables are related.

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Samadhan Ghubade

Senior Biostatistician II at ICON plc
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Correlation is a way to measure the relationship between two things. For example the amount of time you spend studying and your marks. If they tend to increase or decrease together, we say they are correlated. +ve Correlation: When one variable goes up, the other goes up too. -ve Correlation: When one variable goes up, the other goes down. No Correlation: When changes in one variable do not predict changes in the other. Correlation measured by a number called the correlation coefficient, which ranges from -1 to 1 1 means perfect positive correlation (both variables move together exactly). -1 means perfect negative correlation (one variable increases exactly as the other decreases). 0 means no correlation.

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Cristiano Natal Tonéis

Professor Doutor (Educa??o Matemática) - Professor Gradua??o - Professor Universitário; Ensino e Pesquisa. Pós-Gradua??o. Postdoc.
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a correla??o pode ser definida como a rela??o mútua entre dois termos.Embora possuam explica??es e aplica??es similares, a covariancia e a correla??o se diferenciam em um ponto fundamental. Enquanto as variáveis da correla??o se movem de maneira padronizada — seja em sentido positivo ou em sentido contrário —, as da covariancia podem, teoricamente, variar de menos infinito a mais infinito.

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3 Interpreting Values

When interpreting covariance and correlation values, context is crucial. A large positive covariance means the variables tend to increase together, but without a scale, it's hard to judge its significance. Correlation values are easier to interpret. A high positive correlation, close to 1, suggests a strong relationship where variables move in tandem. A high negative correlation means they move in opposite directions. A value near 0 indicates no linear relationship. This standardized scale of correlation makes it universally understandable.

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4 Practical Examples

Let's consider practical examples to illustrate these concepts. Imagine you're comparing hours spent at the gym to weight loss. If your covariance is positive, generally, more gym time associates with more weight loss. However, without knowing how weight loss varies with gym time, it's hard to plan your fitness routine. That's where correlation comes in handy. If the correlation is high, you can confidently say that increasing gym time is likely to lead to weight loss, giving you a clearer picture for decision-making.

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5 Choosing Metrics

In real-world scenarios, choosing between covariance and correlation depends on your need for detail. If you're only interested in knowing whether there's a general trend between sales and advertising budget, covariance might suffice. However, if you need to understand the strength of this relationship to make informed decisions about how much to spend on advertising, correlation provides a more precise and useful measure. Correlation is typically preferred because it gives actionable insights into the relationship between variables.

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6 Statistical Software

For those who are not keen on crunching numbers manually, statistical software can be a lifesaver. Modern programs can calculate both covariance and correlation with simple commands. For example, in Python's Pandas library, you can calculate covariance using dataframe.cov() and correlation with dataframe.corr() . These tools allow you to focus more on interpreting the results rather than getting bogged down in the calculation process.

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Cristiano Natal Tonéis

Professor Doutor (Educa??o Matemática) - Professor Gradua??o - Professor Universitário; Ensino e Pesquisa. Pós-Gradua??o. Postdoc.
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software R para calculos estatisticos. A linguagem R é amplamente utilizada para análise estatística e gráficos. As principais características da linguagem R s?o: Análise de dados: R tem várias fun??es e pacotes para limpar, manipular e analisar dados, incluindo análise de séries temporais e suporte para modelos lineares e n?o lineare

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How do you explain the difference between covariance and correlation to a non-statistician?

1

2

3

4

5

6

7

1 Covariance Basics

2 Correlation Defined

3 Interpreting Values

4 Practical Examples

5 Choosing Metrics

6 Statistical Software

7 Here’s what else to consider

Statistics

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How do you explain the difference between covariance and correlation to a non-statistician?

1

2

3

4

5

6

7

1 Covariance Basics

2 Correlation Defined

3 Interpreting Values

4 Practical Examples

5 Choosing Metrics

6 Statistical Software

7 Here’s what else to consider

Statistics

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