RPubs link information

• RPubs link to presentation (see here)

Introduction

• The following study is based on understanding how human senses influence on the sense of rhythm. In this particular case we analyse the incidence of sight on hand rhythm.

Problem Statement

• The critical question to answer is whether we get lost without the sense of sight, or we can actually keep on track with even rhythm.
• To conduct this test and find a suitable answer, we will follow some basic steps:
  • Collect meaningful samples.
  • Process the collected data accurately.
  • Realise descriptive statistics and basic visualisation in order to understand the data.
  • Conduct one-sample t-test to check whether information suits our needs.
  • Conduct two independen samples hypotesis test to answer our main question.

Data

Data Collection

• Two people (different genders) and two tests performed in different situations to keep them as independent as possible.
• The test was performed with an online stopwatch.
• Each person performed the following tests:
  1. Maintain a 3-second rhythm, by hiting the “Split” button each 3 seconds during 2.5 minutes (50 times). For this first test, the performer was supposed to be watching at the screen.
  2. Repeat the first test, but this time without watching the screen.

Data Cont.

Data Processing

# Data reading:
Stopwatch <- read.csv('C:/Users/Alfredo/Documents/Stopwatch_data.csv')

Data was generated online and copied to Ms Excel, where the rest of the variables had been added for each testing. From Excel, a .csv file was created and imported into RStudio.

Variables

• Shot: hit number in order.
• Time: hit exact time (3 decimals).
• Gender: 1 (factor: “Female”), or 0 (factor:“Male”).
• Watching: indicates whether the test was watching at the screen or not. 1 (factor: “Yes”), or 0 (factor:“No”).

Stopwatch$Gender <- Stopwatch$Gender %>% factor(levels=c(1,0), labels=c('Female','Male'))
Stopwatch$Watching <- Stopwatch$Watching %>% factor(levels=c(1,0), labels=c('Yes','No'))

Descriptive Statistics and Visualisation

• As a first apporach we make sure to be on rhythm for both cases (watching or not). The method is start checking descriptive statistics where we assess whether the data worth analysing. For this case, both are close enough to 3.000, with surpising means.

Stopwatch %>% group_by(Watching) %>% summarise(Min = min(Time, na.rm=TRUE),
                                               Q1 = quantile(Time,probs= .25, na.rm=TRUE),
                                               Median = median(Time, na.rm=TRUE),
                                               Q3 = quantile(Time,probs= .75, na.rm=TRUE),
                                               Max = max(Time, na.rm=TRUE),
                                               Mean = mean(Time, na.rm=TRUE),
                                               SD = sd(Time, na.rm=TRUE),
                                               n=n(),
                                               Missing=sum(is.na(Time)))

Decsriptive Statistics Cont.

• In addition we use a boxplot for understanding data behaviour. As expected, “watching” case is closer to 3.000, while “not watching” has a much wider range of data.

boxplot(Time~Watching, data=Stopwatch, ylab="Reaction time", xlab="Watching status")
abline(h=3.000, col="red")

Hypothesis Testing

• We will be running two hypotesis tests:
  1. One-sample t-test to define whether rhythm while “watching” makes sense. \[H_0: \mu = 3.000 \] \[H_A: \mu \ne 3.000\]
  2. Two independet samples t-test to define whether “not watching” affects rhythm. \[H_0: \mu_1 = \mu_2 \] \[H_A: \mu_1 \ne \mu_2\]

Hypothesis Testing Cont.

Normality Assumption

• For checking data normal distribution as assumed, we use a Q-Q Plot. The first plot corresponds to “watching” data. Its distribution is clearly normal as it follow the straight red line.

Watching_Y <- Stopwatch %>% filter(Watching=="Yes")
Watching_Y$Time %>% qqPlot(dist="norm")

• Initially, it is not the same case for “not watching sample” as some dots are outside the dashed red line. However, considering the sample size n>30, we can assume normality.

Watching_N <- Stopwatch %>% filter(Watching=="No")
Watching_N$Time %>% qqPlot(dist="norm")

Hypothesis Testing Cont.

Variance Homogeneity assumption

• We conduct a Levene Test, where we find p=0.055 > 0.05. For this reason we can assume homogeneity of variance and run the test.

leveneTest(Time~Watching, data=Stopwatch)

Hypothesis Testing Cont.

1. One-sample t-test

TimeWatching <- Stopwatch %>% filter(Watching == 'Yes')

t.test(TimeWatching$Time, mu=3.000)

## 
##  One Sample t-test
## 
## data:  TimeWatching$Time
## t = 0.78579, df = 99, p-value = 0.4339
## alternative hypothesis: true mean is not equal to 3
## 95 percent confidence interval:
##  2.954033 3.106247
## sample estimates:
## mean of x 
##   3.03014

2. Two independet samples t-test

testing <- t.test(
  Time~Watching,
  data=Stopwatch,
  var.equal=TRUE,
  alternative="two.sided"
  )
testing

## 
##  Two Sample t-test
## 
## data:  Time by Watching
## t = 0.47167, df = 198, p-value = 0.6377
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.08435911  0.13739911
## sample estimates:
## mean in group Yes  mean in group No 
##           3.03014           3.00362

Discussion

1. One-sample t-test: Our decision should be to fail to reject H0: mu = 3.000 secs as the p = 0.4339 > 0.05 and the 95% CI of the estimated population mean 3.030 secs was (2.954, 3.106), which captures mu = 3.000. The results of the one-sample t-test were not statistically significant. This meant that the mean time of rhyhtm while watching was similar to the 3.000 secs stated.

2. Two independet samples t-test: Our decision should be to fail to reject H0: mu1 = mu2 as the p = 0.6377 > 0.05 and the 95% CI of the estimated population difference (-0.084, 0.137), which captures H0: mu1 - mu2 = 0. The results of the two-sample t-test were not statistically significant. This meant that the mean time of rhyhtm while watching was not too different to the mean time of rhythm while not watching.

• The conclusion is the finding that sight does not affect dramatically the hability of maintain a certain rhythm.
• Next steps are performing the same analysis while affecting different human senses.