Communicating Statistical Results and Uncertainty
When you report statistical results, your goal is to present findings clearly, honestly, and with attention to uncertainty. Always include the following elements:
- Estimates: report the main effect or parameter of interest, such as a mean difference or regression coefficient;
- Confidence intervals: present interval estimates (such as 95% confidence intervals) to convey the range of plausible values for your estimate;
- P-values: if hypothesis tests are performed, report the exact p-value, not just whether it is "significant";
- Assumptions: state the assumptions underlying your analysis (for example, normality, independence, or equal variances).
Transparency in these elements allows others to understand your results, assess their reliability, and interpret findings appropriately.
1234567891011# Simulate some data for regression set.seed(42) x <- rnorm(100, mean = 10, sd = 2) y <- 5 + 0.8 * x + rnorm(100, sd = 3) model <- lm(y ~ x) # Summarize the model summary(model) # Compute confidence intervals for the coefficients confint(model)
When communicating uncertainty in your results, always highlight both the point estimate and the confidence interval, making it clear that your findings are not exact but reflect a range of plausible values. Avoid overstating the meaning of p-values; a small p-value does not prove a hypothesis, and a large p-value does not prove the absence of an effect. Instead, describe what the data suggest, considering the width of the confidence interval and the practical significance of the estimate. Always discuss the assumptions of your analysis and any limitations that might affect interpretation. This approach maintains statistical rigor and helps your audience draw appropriate conclusions from your results.
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Can you explain what the regression results mean in simple terms?
What assumptions should I check for this regression analysis?
How should I interpret the confidence intervals and p-values in this output?
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When you report statistical results, your goal is to present findings clearly, honestly, and with attention to uncertainty. Always include the following elements:
- Estimates: report the main effect or parameter of interest, such as a mean difference or regression coefficient;
- Confidence intervals: present interval estimates (such as 95% confidence intervals) to convey the range of plausible values for your estimate;
- P-values: if hypothesis tests are performed, report the exact p-value, not just whether it is "significant";
- Assumptions: state the assumptions underlying your analysis (for example, normality, independence, or equal variances).
Transparency in these elements allows others to understand your results, assess their reliability, and interpret findings appropriately.
1234567891011# Simulate some data for regression set.seed(42) x <- rnorm(100, mean = 10, sd = 2) y <- 5 + 0.8 * x + rnorm(100, sd = 3) model <- lm(y ~ x) # Summarize the model summary(model) # Compute confidence intervals for the coefficients confint(model)
When communicating uncertainty in your results, always highlight both the point estimate and the confidence interval, making it clear that your findings are not exact but reflect a range of plausible values. Avoid overstating the meaning of p-values; a small p-value does not prove a hypothesis, and a large p-value does not prove the absence of an effect. Instead, describe what the data suggest, considering the width of the confidence interval and the practical significance of the estimate. Always discuss the assumptions of your analysis and any limitations that might affect interpretation. This approach maintains statistical rigor and helps your audience draw appropriate conclusions from your results.
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