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rstatisticsmeanemmeans
danielb
danielb

Reputation: 23

Why am I getting different means using different functions in R?

I have data showing beta values (neural activity) as a continuous dv and a categorical iv (Position) with several levels (1, 2, 3). I have created a summary dataframe that includes the means for each condition.

    df_sum <- df %>%
  group_by(Position) %>%
  summarise( 
    n=n(),
    mean=mean(Beta),
    sd=sd(Beta)
  ) %>%
  mutate( se=sd/sqrt(n))  %>%
  mutate( ic=se * qt((1-0.05)/2 + .5, n-1))

This is a reanalysis of some old data originally analysed in SPSS, and the means from the summarise function agree with those previously reported. However, when I run t-tests with either emmeans

emmeans((lm(Beta ~ Position, data = df)), pairwise ~ Position)

or t.test

t.test(df$Beta[df$Position=="1"], df$Beta[df$Position=="2"])

the output reports means that are the same as each other but slightly different to the ones calculated by summarise and reported by the original study. Why is this happening (or really, how??), and which should I use?

Upvotes: 1

Views: 180

Answers (1)

Russ Lenth
Russ Lenth

Reputation: 6830

I suspect that you are seeing means that are identical, but the confidence intervals for them differ. And that's because the emmeans results are based on the model fitted by lm, which estimates a common error SD, with more degrees of freedom. Either set of results is fine, but they are based in different models. If he SDs don't differ statistically, you are better off with the lm results because they make more efficient use of the data.

You can reproduce the SEs provided by emmeans as follows:

df_sum %>% 
    mutate(sp = sqrt(sum((n-1)*sd^2) / sum(n-1))) %>%
    group_by(Position) %>%
    mutate(se.p = sp/sqrt(n))

In these steps, we

  1. compute the pooled SD, sp via a weighted average of the variances
  2. Divide into groups
  3. Compute se.p, the SE based on the pooled s

Upvotes: 2

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