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| # Between-Subjects Welch's t-test | ||
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| **between-subjects Welch's t-test:** Compare two groups or conditions where the participants are different in each group and have not been matched or are only matched on broad demographics, e.g. only age. | ||
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| ## The Worked Example | ||
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| ```{r we, echo = FALSE} | ||
| set.seed(1410) | ||
| mx <- runif(1, 0, 100) %>% round2(2) | ||
| sdx <- runif(1, 0, 5) %>% round2(2) | ||
| N <- seq(10, 100, 2) %>% sample(1) | ||
| dat <- tibble(Group = rep(c("A","B"), each = N/2), | ||
| scores = rnorm(N, mx, sdx)) %>% | ||
| mutate(scores = scores + rep(c(0,2), each = N/2)) | ||
| desc <- dat %>% | ||
| group_by(Group) %>% | ||
| summarise(Npg = n(), | ||
| Means = mean(scores) %>% round2(2), | ||
| SDs = sd(scores) %>% round2(2), | ||
| Variance = var(scores) %>% round2(2), | ||
| `Standard Err.` = (SDs/sqrt(Npg)) %>% round2(2)) | ||
| sdp <- sqrt((((N/2 - 1) * desc$SDs[1]^2) + ((N/2 - 1) * desc$SDs[2]^2))/(N/2 + N/2 - 2)) | ||
| t.value <- ((desc$Means[1] - desc$Means[2])/(sdp * sqrt(((1/(N/2)) + (1/(N/2)))))) %>% round2(2) | ||
| cohensd <- ((2* t.value)/sqrt(N-2)) %>% round2(2) | ||
| results <- t.test(dat %>% filter(Group == "A") %>% pull(scores), | ||
| dat %>% filter(Group == "B") %>% pull(scores), | ||
| var.equal = TRUE) %>% | ||
| tidy() %>% | ||
| mutate(cohensd_t = (2*statistic)/sqrt(parameter)) | ||
| ``` | ||
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| Here is your data: | ||
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| ```{r, echo = FALSE} | ||
| desc %>% | ||
| select(-Variance, -`Standard Err.`) %>% | ||
| rename(N = Npg, Mean = Means, SD = SDs) %>% | ||
| knitr::kable(align = "c") | ||
| ``` | ||
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| Let's look at the main t-test formula for Welch's t-test: | ||
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| $$t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$ | ||
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| **Degrees of Freedom** | ||
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| $$df = \frac{\left(\frac{s^2_{x_1}}{n_1}+\frac{s^2_{x_2}}{n_2}\right)^2}{\frac{\left(\frac{s^2_{x_1}}{n_1}\right)^2}{n_1 - 1}+\frac{\left(\frac{s^2_{x_2}}{n_2}\right)^2}{n_2 - 1}}$$ | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,43 @@ | ||
| # Between-Subjects Welch's t-test | ||
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| **between-subjects Welch's t-test:** Compare two groups or conditions where the participants are different in each group and have not been matched or are only matched on broad demographics, e.g. only age. | ||
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| ## The Worked Example | ||
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| Here is your data: | ||
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| <table> | ||
| <thead> | ||
| <tr> | ||
| <th style="text-align:center;"> Group </th> | ||
| <th style="text-align:center;"> N </th> | ||
| <th style="text-align:center;"> Mean </th> | ||
| <th style="text-align:center;"> SD </th> | ||
| </tr> | ||
| </thead> | ||
| <tbody> | ||
| <tr> | ||
| <td style="text-align:center;"> A </td> | ||
| <td style="text-align:center;"> 18 </td> | ||
| <td style="text-align:center;"> 25.58 </td> | ||
| <td style="text-align:center;"> 2.25 </td> | ||
| </tr> | ||
| <tr> | ||
| <td style="text-align:center;"> B </td> | ||
| <td style="text-align:center;"> 18 </td> | ||
| <td style="text-align:center;"> 29.07 </td> | ||
| <td style="text-align:center;"> 2.53 </td> | ||
| </tr> | ||
| </tbody> | ||
| </table> | ||
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| Let's look at the main t-test formula for Welch's t-test: | ||
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| $$t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$ | ||
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| **Degrees of Freedom** | ||
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| $$df = \frac{\left(\frac{s^2_{x_1}}{n_1}+\frac{s^2_{x_2}}{n_2}\right)^2}{\frac{\left(\frac{s^2_{x_1}}{n_1}\right)^2}{n_1 - 1}+\frac{\left(\frac{s^2_{x_2}}{n_2}\right)^2}{n_2 - 1}}$$ | ||
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