t-Test HW

Author

Cionna Freeman

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

People with higher levels of income will report less stress. *

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$income, useNA = "always")

         1 low       2 middle         3 high rather not say           <NA> 
           479            434            243            436              0 
# # note that the table() output shows you exactly how the levels of your variable are rewritten. 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, income != "rather not say")
d <- subset(d, income != "2 middle")








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

 1 low 3 high   <NA> 
   479    243      0 
# 
# # check your variable types
str(d)
'data.frame':   722 obs. of  6 variables:
 $ income    : chr  "1 low" "3 high" "1 low" "1 low" ...
 $ edu       : chr  "2 Currently in college" "2 Currently in college" "2 Currently in college" "5 Completed Bachelors Degree" ...
 $ swb       : num  5.5 5 4.67 5.33 5.17 ...
 $ moa_safety: num  3.25 2.75 3 2.75 3.5 3.25 3.5 3.5 3.75 2.75 ...
 $ stress    : num  2.4 2.9 3.5 4.4 2.8 3 3 3.3 3.1 2.5 ...
 $ pipwd     : num  3.53 3 3 3 2.33 ...
# 
# # make sure that your IV is recognized as a factor by R
d$income<- as.factor(d$income)

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(stress~income, data = d)
Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)
group   1  1.4734 0.2252
      720

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$stress)
# # use it to check the skew and kurtosis of your DV
describe(d$stress)
   vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
X1    1 722  3.1 0.62    3.1    3.09 0.59 1.4 4.7   3.3 0.06    -0.32 0.02
# 
# # 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$stress, group=d$income)

 Descriptive statistics by group 
group: 1 low
   vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
X1    1 479 3.09 0.61    3.1    3.09 0.59 1.4 4.6   3.2 0.03    -0.24 0.03
------------------------------------------------------------ 
group: 3 high
   vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
X1    1 243 3.11 0.64      3     3.1 0.59 1.6 4.7   3.1 0.12    -0.49 0.04
# 
# # also use a histogram to examine your continuous variable
hist(d$stress)

# 
# # last, use a boxplot to examine your continuous and categorical variables together
boxplot(d$stress~d$income)

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.

We dropped middle income participants and prefer not to say participants. We also confirmed the homogenity of variance using Levene’s Test. (p-.224) and that our dependent variable is normally distributed (skew and kurtosis 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$stress~d$income)

View Test Output

t_output

    Welch Two Sample t-test

data:  d$stress by d$income
t = -0.34692, df = 466.73, p-value = 0.7288
alternative hypothesis: true difference in means between group 1 low and group 3 high is not equal to 0
95 percent confidence interval:
 -0.1148370  0.0803739
sample estimates:
 mean in group 1 low mean in group 3 high 
            3.089353             3.106584

Calculate Cohen’s d

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

View Effect Size

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

Cohen's d

d estimate: -0.02774588 (negligible)
95 percent confidence interval:
     lower      upper 
-0.1823764  0.1268846

Write Up Results

We tested our hypothesis that high income would report significantly less stress than low income using a Welch Two sample t-test. Our data met all of my assumptions of a t-test, however, we did not find significant difference, t (466.73)- 0.347, p-.072, d-.028, 95% (-0.11,.08). (refer to figure 1)

Our effect size was trivial according to Cohen (1988).

References

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