t-Test HW

Author

Maria Amanda Irias

Loading Libraries

library(psych) # for the describe() command
library(car) # for the leveneTest() command
library(effsize) # for the cohen.d() command

Importing Data

d <- read.csv(file="Data/mydata.csv", header=T)

State Your Hypothesis - PART OF YOUR WRITEUP

Women will report more symptoms of neuroticism than men.

State your t-test hypothesis. Remember, a t-test has one continuous variable as the dependent variable, and one categorical variable with two levels as the independent variable. If your IV of choice has more than one level, you will need to pick two levels to compare and drop the rest, or combine levels until you only have two left.

Check Your Assumptions

T-test Assumptions

  • Data values must be independent (independent t-test only) (confirmed by data report)
  • Data obtained via a random sample (confirmed by data report)
  • IV must have two levels (will check below)
  • Dependent variable must be normally distributed (will check below. if issues, note and proceed)
  • Variances of the two groups must be approximately equal, aka ‘homogeneity of variance’. Lacking this makes our results inaccurate (will check below - this really only applies to Student’s t-test, but we’ll check it anyway)

Checking IV levels

# # preview the levels and counts for your IV
table(d$gender, useNA = "always")

            female I use another term               male  Prefer not to say 
               929                 31                179                 19 
              <NA> 
                 0 
# 
# # note that the table() output shows you exactly how the levels of your variable are written. when recoding, make sure you are spelling them exactly as they appear
# 
# # to drop levels from your variable
# # this subsets the data and says that any participant who is coded as 'LEVEL BAD' should be removed
# # if you don't need this for the homework, comment it out (add a # at the beginning of the line)
d <- subset(d, gender != "I use another term")
d <- subset(d, gender != "Prefer not to say")

# 
# # to combine levels
# # this says that where any participant is coded as 'LEVEL BAD' it should be replaced by 'LEVEL GOOD'
# # you can repeat this as needed, changing 'LEVEL BAD' if you have multiple levels that you want to combine into a single level
# # if you don't need this for the homework, comment it out (add a # at the beginning of the line)


# 
# # preview your changes and make sure everything is correct
table(d$gender, useNA = "always")

female   male   <NA> 
   929    179      0 
# 
# # check your variable types
str(d)
'data.frame':   1108 obs. of  6 variables:
 $ edeq12            : num  1.58 1.83 1 1.67 1.42 ...
 $ big5_neu          : num  6 6.67 4 4 2.67 ...
 $ gender            : chr  "female" "male" "female" "female" ...
 $ iou               : num  3.19 4 1.59 3.37 1.7 ...
 $ sexual_orientation: chr  "Heterosexual/Straight" "Heterosexual/Straight" "Heterosexual/Straight" "Heterosexual/Straight" ...
 $ rse               : num  2.3 1.6 3.9 1.7 3.9 2.4 1.8 3.5 2.6 3 ...
# 
# # make sure that your IV is recognized as a factor by R
 d$gender <- as.factor(d$gender)

Testing Homogeneity of Variance with Levene’s Test

We can test whether the variances of our two groups are equal using Levene’s test. The null hypothesis is that the variance between the two groups is equal, which is the result we want. So when running Levene’s test we’re hoping for a non-significant result!

# # use the leveneTest() command from the car package to test homogeneity of variance
# # uses the same 'formula' setup that we'll use for our t-test: formula is y~x, where y is our DV and x is our IV
 leveneTest(big5_neu~gender, data = d)
Levene's Test for Homogeneity of Variance (center = median)
        Df F value  Pr(>F)  
group    1  4.0408 0.04466 *
      1106                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

This is more of a formality in our case, because we are using Welch’s t-test, which does not have the same assumptions as Student’s t-test (the default type of t-test) about variance. R defaults to using Welch’s t-test so this doesn’t require any extra effort on our part!

Check Normality

# you only need to check the variables you're using in the current analysis
# although you checked them previously, it's always a good idea to look them over again and be sure that everything is correct

# you can use the describe() command on an entire datafrom (d) or just on a single variable (d$pss)
# use it to check the skew and kurtosis of your DV
describe(d$big5_neu)
   vars    n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 1108 4.34 1.52   4.67    4.39 1.48   1   7     6 -0.27     -0.8 0.05
# can use the describeBy() command to view the means and standard deviations by group
# it's very similar to the describe() command but splits the dataframe according to the 'group' variable
describeBy(d$big5_neu, group=d$gender)

 Descriptive statistics by group 
group: female
   vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 929 4.47 1.48   4.67    4.53 1.48   1   7     6 -0.35    -0.68 0.05
------------------------------------------------------------ 
group: male
   vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
X1    1 179  3.7 1.57   3.67    3.65 1.98   1   7     6 0.22    -0.91 0.12
# also use a histogram to examine your continuous variable
hist(d$big5_neu)

# last, use a boxplot to examine your continuous and categorical variables together *conyinous DV on left
boxplot(d$big5_neu~d$gender)

Issues with My Data - PART OF YOUR WRITEUP

Briefly describe any issues with your data and how you’ve resolved them. For instance, if you are using a gender variable that has three levels, you should say that you dropped or combined two of the levels for your analysis. This should be written in an appropriate scientific tone.

A note that might be helpful: the opposite of ‘homogeneity of variance’ (the thing we want) is ‘heterogeneity of variance’ (the thing we don’t want). So, you could say something like this, if needed:

“Before proceeding with analysis, we confirmed that all t-test assumptions were met. Levene’s test found significant heterogeneity of variance (p = .###). As a result, Welch’s t-test will be used.”

We dorpped participants who identifies as something other than Man or Woman and also dropped those who chose to not say their gender identity. We also confirmed homogeneity of variance (p= 0.047) and that our dependent variable is normally distributed between -2 and 2.

Run a T-test

# # very simple! we specify the dataframe alongside the variables instead of having a separate argument for the dataframe like we did for leveneTest()
t_output <- t.test(d$big5_neu~d$gender)

View Test Output

 t_output

    Welch Two Sample t-test

data:  d$big5_neu by d$gender
t = 6.0049, df = 242.41, p-value = 6.953e-09
alternative hypothesis: true difference in means between group female and group male is not equal to 0
95 percent confidence interval:
 0.5121625 1.0122014
sample estimates:
mean in group female   mean in group male 
            4.466093             3.703911

Calculate Cohen’s d

# # once again, we use our formula to calculate cohen's d
d_output <- cohen.d(d$big5_neu~d$gender)

View Effect Size

  • Trivial: < .2
  • Small: between .2 and .5
  • Medium: between .5 and .8
  • Large: > .8
d_output

Cohen's d

d estimate: 0.511167 (medium)
95 percent confidence interval:
    lower     upper 
0.3495942 0.6727398

Write Up Results

Write up your results. Again, make sure to maintain an appropriate tone, and follow APA guidelines for reporting statistical results. I recommend following the below outline:

  • Briefly restate your hypothesis
  • Describe any issues with your data (you can copy/paste from above, just make sure everything flows).
  • Report your results. Remember to include means of your groups, your t-value, your degrees of freedom, your p-value, your d-value, and your confidence interval.
  • If your test is significant, interpret your effect size (trivial, small, medium, or large) and include the citation.
  • Make sure to include a reference to Figure 1 (created using the code below)

We tested our hypothesis that women would report significantly more ssymptoms of neuroticism than men using an independent samples t-test. Our data met all of the assumptions of the t=test, and we did find a significant difference, t(242.41) = 6.00, p = 6.953e-09, d = 0.51, 95% [0.51,1.01]

Our effect size was large according to Cohen (1988) (refer to figure 1)

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.