Keeping nulls straight is the thing I have the most difficulty with, it seems. You're right: no significant difference in means.
d <- data.frame(
p = c(7, 25, 19, 25, 39, 53, 67, 69, 59, 68, 112, 168, 194, 214, 299, 348, 97, 983, 193, 230, 331, 344, 197, 126, 90, 115, 86, 144, 177, 6, 4, 36, 41, 43, 81, 117, 100, 109, 146, 202, 262, 272, 274, 260, 201, 173, 200, 145, 130, 166),
t = factor(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)),
g = factor(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
)
# 1. Between levels of t
t_test <- t.test(p ~ t, data = d)
print(t_test)
#>
#> Welch Two Sample t-test
#>
#> data: p by t
#> t = 1.3773, df = 39.062, p-value = 0.1763
#> alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
#> 95 percent confidence interval:
#> -18.06941 95.20578
#> sample estimates:
#> mean in group 0 mean in group 1
#> 161.5682 123.0000
# 2. Between levels of g
g_test <- t.test(p ~ g, data = d)
print(g_test)
#>
#> Welch Two Sample t-test
#>
#> data: p by g
#> t = -0.80594, df = 31.623, p-value = 0.4263
#> alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
#> 95 percent confidence interval:
#> -122.37102 53.01102
#> sample estimates:
#> mean in group 0 mean in group 1
#> 139.60 174.28
# 3. Between the combinations of t and g
interaction_test <- aov(p ~ t * g, data = d)
summary(interaction_test)
#> Df Sum Sq Mean Sq F value Pr(>F)
#> t 1 7854 7854 0.328 0.570
#> g 1 12670 12670 0.529 0.471
#> t:g 1 4455 4455 0.186 0.668
#> Residuals 46 1101023 23935
Created on 2023-06-09 with reprex v2.0.2
The script performs several statistical tests and an analysis of variance (ANOVA) to explore the relationships between variables in the provided dataset. Let`s interpret the results of each test:
-
Between levels of t:
The code performs a t-test to compare the values of variable p between two levels of t (0 and 1). The output of the t.test function provides information about the test statistic, the p-value, and confidence intervals. Without the actual output, it is difficult to provide specific interpretations. However, in general, if the p-value is less than a chosen significance level (e.g., 0.05), it suggests that there is a statistically significant difference between the two levels of t in terms of variable p.
-
Between levels of g:
Similar to the previous test, this code performs a t-test to compare the values of p between two levels of g (0 and 1). The interpretation of the results is the same as in the previous test. The output of t.test provides the test statistic, p-value, and confidence intervals to assess the statistical significance of the difference between the levels of g in terms of variable p.
-
Between the combinations of t and g:
In this case, the code performs an analysis of variance (ANOVA) using the aov function to examine the interaction effect between t and g on variable p. The summary function is then used to obtain the ANOVA table with relevant statistics such as the F-value and p-value. Without the actual output, it is challenging to provide a specific interpretation. However, the ANOVA table allows you to assess whether there are significant interactions between t and g on the dependent variable p.
Overall, the script aims to analyze the relationships between the variables p, t, and g using t-tests and an ANOVA. The interpretation of the results depends on the specific output generated by the script, including test statistics, p-values, and confidence intervals.
Based on the provided output, let`s interpret the results of the Welch Two Sample t-test and the ANOVA interaction test:
- Welch Two Sample t-test:
The t-test compares the means of two groups (g = 0 and g = 1) for the variable p. Here is the interpretation of the output:
- t-value: -0.80594
- Degrees of freedom (df): 31.623
- p-value: 0.4263
The null hypothesis in this case is that there is no difference in means between the two groups. Since the p-value (0.4263) is greater than the chosen significance level (e.g., 0.05), we do not have enough evidence to reject the null hypothesis. This suggests that there is no statistically significant difference in the means of variable p between group 0 and group 1.
- ANOVA Interaction Test:
The ANOVA test examines the interaction effect between t and g on the dependent variable p. Here is the interpretation of the output:
- F-value and p-value for
t: F = 0.328, p = 0.570
- F-value and p-value for
g: F = 0.529, p = 0.471
- F-value and p-value for interaction
t:g: F = 0.186, p = 0.668
For all three factors (t, g, and t:g), the p-values are greater than the chosen significance level (e.g., 0.05). This suggests that there is no statistically significant interaction effect between t and g on the dependent variable p. In other words, the interaction between t and g does not significantly impact the mean values of p.
Overall, based on the provided output, there is no evidence to suggest significant differences between groups or interaction effects between t and g in terms of the variable p.