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tweak prop.test explanation #2

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tweak prop.test explanation #2

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12 changes: 6 additions & 6 deletions inst/themes/default/prop.test.Rmd
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Original file line number Diff line number Diff line change
Expand Up @@ -86,15 +86,15 @@ stmt3 <-

paste0(
"The observed difference in proportions is ",
x$estimate[2] - x$estimate[1],
signif(x$estimate[2] - x$estimate[1], 3),
". The observed proportion for the first group is ",
x$estimate[1],
signif(x$estimate[1], 3),
" (",
prettyNum(x1, big.mark=","),
" events out of a total sample size of ",
prettyNum(n1, big.mark=","),
"). For the second group, the observed proportion is ",
x$estimate[2],
signif(x$estimate[2], 3),
" (",
prettyNum(x2, big.mark=","),
", out of a total sample size of ",
Expand Down Expand Up @@ -125,8 +125,8 @@ stmt4 <-
}
```

`r stmt1`. Using a significance level of `r 1 - attr(x$conf.int, "conf")`, we `r if (x$p.value < 1 - attr(x$conf.int, "conf")) "reject" else "do not reject"` the null hypothesis, and `r stmt2`. `r stmt3`.
`r stmt1`. Using a significance level of `r 1 - signif(attr(x$conf.int, "conf"), 3)`, we `r if (x$p.value < 1 - signif(attr(x$conf.int, "conf"), 3)) "reject" else "do not reject"` the null hypothesis, and `r stmt2`. `r stmt3`.

The confidence interval for the true `r if (onesamp) "population proportion" else "difference in population proportions"` is (`r tidyx$conf.low`, `r tidyx$conf.high`). This interval will contain the true `r if(onesamp) "population proportion" else "difference in population proportions"` 95 times out of 100.
The confidence interval for the true `r if (onesamp) "population proportion" else "difference in population proportions"` is (`r signif(tidyx$conf.low, 3)`, `r signif(tidyx$conf.high, 3)`). Intervals generated with this procedure will contain the true `r if(onesamp) "population proportion" else "difference in population proportions"` `r round(attr(x$conf.int, "conf.level") * 100)` times out of 100.

The p-value for this test is `r x$p.value`. This, formally, is defined as the probability -- if the null hypothesis is true -- of observing a `r if (onesamp) "sample proportion" else "difference in sample proportions"` that is as or more extreme than the `r if (onesamp) "sample proportion" else "difference in sample proportions"` from this data set. In this case, this is the probability -- if the true `r if (onesamp) paste0("population proportion is ", x$null.value) else "population proportions are equal"` -- of observing a `r if (onesamp) "sample proportion" else "difference in sample proportions"` that is greater than `r stmt4`.
The p-value for this test is `r x$p.value`. In other words: if the true `r if (onesamp) "sample proportion" else "difference in sample proportions"` were exactly `r ifelse(is.null(x$null.value), 0, x$null.value)`, and we collected 100 replicate data sets, we would find a discrepancy this large (or larger) in about `r round(x$p.value * 100)` of these 100 cases.