CI

CI

1. level of confidence of 95% (±1.96 standard errors) is a convenient level for conducting scientific research, so it is used almost universally

   • Note that the 95% CI is statistically the same as setting the p-value as p = 0.05.
     • can be set at other levels, e.g. 99% (±2.57 standard errors) but the 95% CI is the standard one used by most researchers.
     • are used for hypothesis testing but are also useful because they demonstrate how small or large the true effect size might be.

2. following quantities make up and influence a confidence interval and are most important if you are to correctly interpret CIs in research articles:

   • a. The sample mean (or proportion)
     • determines the location or middle of the confidence interval
   • b. The sample size (n).
     • number (n) in the sample increases, the width of the CI gets narrower
     • often described as the “power” of the study
       • it reflects the importance of large numbers of participants in a study sample.
         • narrower the CI, the more certain one can be about the size of the true effect.
     • If a study reports a 95% CI then means that there is a 95% chance that the true result lies within the CI.
       • As the confidence interval gets smaller, the width of the CI gets narrower and your confidence in the results increases.
   • c. The sample standard deviation (s).
     • As the s increases, the width of the CI gets wider.
       • another way of demonstrating the effect of the sample size on the CI.

3. Other factors

   • 1. CI for RR and OR:
     • If the CI around a RR or OR includes one, this result is NOT statistically significant
       • this is because RR = 1 and OR = 1,
         • is the null value for the relative risk and odds ratio.
   • 2. CI for the Mean:
     • If the CI for the mean (eg difference in mean scores between two groups) includes ZERO,
       • this result is NOT statistically significant, as the null value for the mean difference is zero.

4. state how confident we are that the true population mean (or proportion) will fall between the lower and upper limits expressed by the confidence intervals.

   • important, because as researchers, we usually deal with samples from a population
     • show the extent to which statistical estimates (from the sample) could be accurate (or generalisable to the total population of interest).