Nursing research p-values and confidence intervals notes

What does a p-value represent?

The probability of observing the data, or something more extreme, given that the null hypothesis is true.

True or False: A p-value less than 0.05 indicates statistical significance.

True - This means the results are unlikely to have occurred by chance if the null hypothesis is true.

Fill in the blank: A smaller p-value indicates _____ evidence against the null hypothesis.

stronger

How do you interpret a p-value of 0.01?

There is a 1% probability that the observed results are due to chance, suggesting strong evidence against the null hypothesis.

Comparison: p-value vs. Effect Size

p-value measures statistical significance; effect size quantifies the strength of the relationship or difference.

What does a p-value of 0.20 imply?

There is a 20% chance of observing the results if the null hypothesis is true, indicating weak evidence against it.

Cause → Effect: High p-value

A high p-value suggests that the observed data is consistent with the null hypothesis.

When is a p-value considered not significant?

Typically, when it is greater than 0.05, indicating insufficient evidence to reject the null hypothesis.

True or False: A p-value of 0.03 is more significant than 0.04.

True - A smaller p-value indicates stronger evidence against the null hypothesis.

What is the threshold commonly used for significance?

0.05 - Results below this threshold suggest rejecting the null hypothesis.

Example: Store discount calculation

If a store tests a new advertising strategy, a p-value of 0.02 indicates significant sales increase likelihood under this strategy.

Effect of sample size on p-value

Larger sample sizes can lead to smaller p-values, even for trivial effects, influencing interpretation.

How is p-value related to hypothesis testing?

It helps determine whether to reject the null hypothesis based on data evidence.

What does a p-value of 0.50 suggest?

There is insufficient evidence to reject the null hypothesis, indicating that the observed data could easily occur by chance.

Comparison: One-tailed vs. Two-tailed p-value

One-tailed tests assess direction; two-tailed tests assess any significant difference.

Example: Nursing research scenario

In a study, if a new treatment has a p-value of 0.04, it suggests a significant effect compared to standard treatment.

Confidence Interval (CI) definition?

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter. For example, a $\displaystyle 95\\%$ CI provides an estimate of where the parameter lies with $\displaystyle 95\\%$ certainty.

True or False: A wider CI indicates more precision.

False. A wider CI indicates less precision in estimating the population parameter.

How is a CI calculated?

A CI is calculated using the formula: sample mean ± margin of error. The margin of error depends on the standard deviation and sample size.

Fill in the blank: A $\displaystyle 90\\%$ CI is ______ than a $\displaystyle 95\\%$ CI.

narrower; A $\displaystyle 90\\%$ CI has less confidence but is more precise.

What does a $\displaystyle 95\\%$ CI mean?

It means that if we were to take 100 random samples and compute a CI for each, about $\displaystyle 95\\%$ of those intervals would contain the true population parameter.

Confidence Level vs. Width of CI?

Increasing the confidence level increases the width of the CI. Example: A $\displaystyle 99\\%$ CI is wider than a $\displaystyle 95\\%$ CI.

Example: CI for average rent?

If the average rent sampled is $\displaystyle 1,200 with a margin of error of$100, the 95\% CI is ($\displaystyle 1,100,$1,300).

What influences the width of a CI?

The width is influenced by sample size, variability in the data, and the confidence level. Larger samples yield narrower CIs.

True or False: A CI can never contain the true parameter.

False. A CI is an estimate; it can contain or exclude the true parameter, but we accept a certain level of confidence.

Margin of Error meaning?

The margin of error represents the maximum expected difference between the true population parameter and the sample statistic. It determines the width of the CI.

How does sample size affect CI?

Larger sample sizes generally lead to more precise estimates and narrower confidence intervals, reducing the margin of error.

CI for a store's average sales?

If average sales are $\displaystyle 5,000 with a margin of error of$200, the 95\% CI could be ($\displaystyle 4,800,$5,200).

What is a point estimate?

A point estimate is a single value that serves as an estimate of a population parameter. Example: sample mean sales of $4,800.

Comparing two CIs: (A) $\displaystyle 1000-$2000, (B) $\displaystyle 1500-$1700?

CI (B) is narrower but less confident than CI (A) which covers a broader range with more uncertainty.

Confidence intervals use ______ to summarize data.

sample statistics; They help infer about the population parameter based on sample data.

What does the term 'significance' relate to in CI?

Significance in CI relates to whether the interval excludes a value of interest, such as a null hypothesis value.