Lee shrimp data analysis v1

library(tidyverse)
library(lubridate)
library(ggplot2)
library(plotly)

print(c(mean(activity_normal_temp), mean(activity_high_temp)))

[1] 1.666667 1.388889

The means of the activity levels are fairly similar, but it’s still worth conducting a hypothesis test of the differences between these two means.

print(result)

    Two Sample t-test

data:  activity_level by temp_condition
t = -1.0791, df = 34, p-value = 0.2882
alternative hypothesis: true difference in means between group High and group Normal is not equal to 0
95 percent confidence interval:
 -0.8009268  0.2453713
sample estimates:
  mean in group High mean in group Normal 
            1.388889             1.666667 

print(c(median(activity_normal_temp), median(activity_high_temp)))

[1] 2 1

Yep, definitely see different medians of these groups. Because the distributions of activity level for each temperature group are skewed (particularly the high-temp group skewed right), let’s try a median hypothesis test, since medians are more robust to skewness than means are.

Null hypothesis: the medians are the same Alternative hypothesis: the medians are not the same.

print(pvalue)

[1] 0.09978488

Significant at p < 0.1 level! neat! The medians of these two distributions are statistically significantly different at the p < 0.1 level, so we can be confident that were this study repeated 100x, 90 of the outcomes would show significant differences in the median activity levels of these two groups. (90% confidence).

library(dplyr)

selected_data <- shrimp %>% select(temp, activity_level)
contingency_table <- table(selected_data$temp, selected_data$activity_level)
print(contingency_table)

        
          0  1  2  3
  High    0 12  5  1
  Normal  2  5  8  3

# Perform chi-square test
chi_square_test_v1 <- chisq.test(contingency_table)

Warning: Chi-squared approximation may be incorrect

# View the results
print(chi_square_test_v1)

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 6.5747, df = 3, p-value = 0.08676

Again, not significant at p<0.05 level, but YES significant at p < 0.1 level. We might say that the difference in activity level shows a “light trend that would require further investigation to confirm”. Also sometimes phrased as “p < 0.1 as weak evidence or a trend”.

Your paper/poster should also clearly designate what behaviors you termed as each activity level (like, activity level 0 = ????, activity level 1 = ????, etc.)

Let’s try another chi-sq contingency table setup:

print(contingency_table_v2)

        
         high low
  High      6  12
  Normal   11   7

# Perform chi-square test
chi_square_test_v2 <- chisq.test(contingency_table_v2)

# View the results
print(chi_square_test_v2)

    Pearson's Chi-squared test with Yates' continuity correction

data:  contingency_table_v2
X-squared = 1.7833, df = 1, p-value = 0.1817

Nope! That’s worse. Let’s try a different activity grouping - no activity versus any activity at all.

print(contingency_table_v3)

        
         active inactive
  High       18        0
  Normal     16        2

Seems like this is going to be the worst yet, but let’s proceed!

# Perform chi-square test
chi_square_test_v3 <- chisq.test(contingency_table_v3)

Warning: Chi-squared approximation may be incorrect

# View the results
print(chi_square_test_v3)

    Pearson's Chi-squared test with Yates' continuity correction

data:  contingency_table_v3
X-squared = 0.52941, df = 1, p-value = 0.4669

Woof! No good.

Okay, let’s try low activity (0-2) versus high activity (3):

print(contingency_table_v4)

        
         high_activity low_activity
  High               1           17
  Normal             3           15

Seems not so good so far - like the groups have the same activity levels, but anyway let’s try it just to make sure:

# Perform chi-square test
chi_square_test_v4 <- chisq.test(contingency_table_v4)

Warning: Chi-squared approximation may be incorrect

# View the results
print(chi_square_test_v4)

    Pearson's Chi-squared test with Yates' continuity correction

data:  contingency_table_v4
X-squared = 0.28125, df = 1, p-value = 0.5959

Nope! Bad! A very large p-value so this does not indicate a significant difference between treatments.

So, in summary, our best result for chi-squared analysis of activity level on temperature uses all the activity levels as distinct.

Okay, now let’s model activity level on all the recorded factors and see what we can see: