Confidence Intervals 🌵

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<a href="https://psychmethods.github.io/coursenotes/" target="_blank">Methods in Psychological Research</a>
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# Confidence Intervals

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# Confidence Intervals (CI)

.pull-left[
- Sample statistics estimate population parameters
- How confident are we in these estimations?
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.pull-right[
- Confidence interval
  - range around sample statistic in which the corresponding population parameter is estimated to be.
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# Confidence Intervals (CI)

.pull-left[
- Sample statistics typically deviate from actual population parameters
- Wake students, n = 100; MIQ = 136
- Is mean Wake IQ really 136?
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.pull-right[
- Confidence interval: 
  - Given sample size and statistic,
  - we're X% confident that the population parameter is within this range
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# Confidence Intervals (CI)

- CIs are computed with specific percentages
- Most common: 95% confidence interval

> “…sample mean of 5.5, 95% CI[4.2, 6.8]…”

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> “If the study were repeated with different samples, the population mean would fall within the interval 95% of the time.”

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# Demo
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<iframe style="overflow: hidden;" src="https://wise1.cgu.edu/vis/ci_creation/" width="750" height="600" frameborder="0"</iframe>  
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# Wrapping Up...

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# Practicalities

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# What's needed to compute CIs?

- Standard error of the mean (SE)
  - How much will this statistic vary from sample to sample, on average? 
- As N increases `\(\rightarrow\)` SE decreases `\(\rightarrow\)` CI narrows
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- Confidence % (you set this)
  - 95%, then look at ± 1.96 SEs
  - 99%, then look at ± 2.58 SEs

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## Interpreting CIs

- In results, will generally report lower and upper CIs:

> “Mean IQ score was 136, 95% CI [130, 142].”

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- There's an important link between CIs and statistical significance
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- `\(H_{0}\)`: r = 0
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- Sig test: How unusual this observed r is
  - assuming r = 0?
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- If p `\(\lt\)` .05, 
  - reject `\(H_{0}\)`
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- There's an important link between CIs and statistical significance
- `\(H_{0}\)`: r = 0
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- CI: Are we 95%+ confident that r is not 0?
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- If 95% CI does not include 0
  - reject `\(H_{0}\)`

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- There's an important link between CIs and statistical significance
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- We can say:
> “…the 95% CI does not contain zero, and so X and Y were positively correlated.”

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- There's an important link between CIs and statistical significance
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- We can say:
> “…the 95% CI contains zero and so the correlation was not statistically significant…”

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## Circling back

.pull-left[
- Wake students, n = 100; MIQ = 136
- American population, MIQ = 98
- Are Wake students different than the American pop.? 
]
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.pull-right[
- How unusual would 136 IQ in the sample,
  - assuming MWFU-IQ = MUSA-IQ?
- Is p < .05?

- What is the 95% CI for MWFU-IQ?
  - Does it include 98?
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# Wrapping Up...