A medical statistician wanted to examine the relationship between the amount of
sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight counties around the country.
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To examine the relationship between the amount of sunshine and the incidence of skin cancer, the medical statistician conducted an experiment by collecting data from eight different counties. The data consisted of two variables: the number of skin cancers detected per 100,000 of the population (y) and the average daily sunshine in each county (x).
To analyze this data and understand the relationship between these two variables, the statistician can follow these steps:
Step 1: Data Collection
Collect the data for the number of skin cancers detected per 100,000 of the population and the average daily sunshine in each of the eight counties. Ensure that the data is accurate and representative of the population.
Step 2: Data Analysis
Analyze the data using appropriate statistical methods. Some common methods include scatter plots, correlation coefficients, and regression analysis.
Step 3: Scatter Plot
Create a scatter plot with the average daily sunshine (x-axis) and the number of skin cancers per 100,000 of the population (y-axis). Each data point represents a county. This plot will help visualize the relationship between the two variables.
Step 4: Correlation Coefficient
Calculate the correlation coefficient (typically denoted as r) to quantify the strength and direction of the relationship between the two variables. The value of r ranges from -1 to +1. A positive value indicates a positive relationship, while a negative value indicates a negative relationship. The closer the value is to 1 or -1, the stronger the relationship. A value close to 0 indicates a weak or no relationship.
Step 5: Regression Analysis
Perform a regression analysis to determine the equation of the regression line or curve that best fits the data. This equation can be used to predict the number of skin cancers based on the amount of sunshine.
Step 6: Interpretation
Interpret the results of the analysis. This includes assessing the strength and significance of the relationship between the amount of sunshine and the incidence of skin cancer, as well as any other observations or patterns found in the data.
By following these steps, the medical statistician can examine the relationship between the amount of sunshine and the incidence of skin cancer and draw meaningful conclusions from the data.
To examine the relationship between the amount of sunshine (x) and the incidence of skin cancer (y), a medical statistician conducted an experiment. The statistician collected data on the number of skin cancers detected per 100,000 of the population and the average daily sunshine in eight counties around the country.
To analyze the relationship between these two variables, the statistician could use a statistical technique called regression analysis. Regression analysis helps in determining the relationship between a dependent variable (skin cancer incidence) and one or more independent variables (average daily sunshine).
Here are the steps the statistician could follow to conduct regression analysis:
1. Data Collection: The statistician has already collected the data on the number of skin cancers and average daily sunshine in each county.
2. Data Preparation: The data should be organized in a table or spreadsheet format, with one column for the skin cancer incidence and another column for the average daily sunshine. Make sure to label the columns appropriately for clarity.
3. Variable Selection: Determine which variable will be treated as the dependent variable (y) and which will be treated as the independent variable (x). In this case, skin cancer incidence (number of skin cancers per 100,000 of the population) will be the dependent variable (y), and average daily sunshine will be the independent variable (x).
4. Regression Analysis: Use statistical software like Excel, SPSS, R, or Python to perform the regression analysis. The software will calculate the regression equation that best fits the relationship between the variables. This equation can be used to predict the skin cancer incidence based on the average daily sunshine.
5. Interpretation: Analyze the results of the regression analysis. Look at measures such as the coefficient of determination (R-squared), the p-value, and the coefficients for the independent variable(s) to understand the strength and significance of the relationship between average daily sunshine and skin cancer incidence. The R-squared value indicates the proportion of the variation in skin cancer incidence that can be explained by average daily sunshine.
Remember that correlation does not imply causation. Even if a statistical relationship is found between average daily sunshine and skin cancer incidence, it does not necessarily mean that sunshine causes skin cancer. Other factors such as genetics, sunscreen usage, and environmental factors could also play a significant role.
By following these steps, the medical statistician can examine the relationship between the amount of sunshine and the incidence of skin cancer and gain insights into this important health issue.