Data Analysis and visualization in R

Project: “Multifinality”

1. Dataset description

1.1 How did you obtain the dataset?

I used the data from my bachelor thesis “Multifinality: Seven at a stroke - Perception of effort of unifinal vs. multifinal means of goal achievement.” For four different sports products (rope, hometrainer, handballs, treadmill), the participants estimated how strenous and precious they were.

1.2 How were the data originally collected?

The data were collected online. I used soscisurvey (a free tool) to create the questionnaire. The questionnaire was filled out online by 226 participants coming from Germany or Switzerland.

1.3 How many rows and columns are in the dataset?

The dataset contains 226 rows and 144 columns. For this paper, I analyzed 226 rows and 16 different columns of the dataset.

1.4 What are the columns in the dataset? For each column, give the variable name and a brief description of what it represents.

Dependent variables

I focused on the construct effort and value as dependent variables. Four items measured the effort and value perception. The same items were used in order to evaluate each of the four sports products (rope, hometrainer, handballs, treadmill).

Effort Scale:

The use of this product requires physical energy.
The use of this product is strenous.
It is tiring to use this product.

One item of the effort scale (The use of this product comes with high effort) was excluded to get a better Chronbach’s Alpha.

The Cronbach’s Alpha of the effort scale for the different sports products was as follows: alpha rope = .66, alpha hometrainer = .73, alpha handballs = .82 , alpha treadmill = .74.

Mean_Effort1: Effort perception of the first sports product: rope (t1).
Mean_Effort2: Effort perception of the second sports product: hometrainer (t2).
Mean_Effort3: Effort perception of the third sports product: handballs (t3).
Mean_Effort4: Effort perception of the fourth sports product: treadmill (t4).

Value Scale:

The quality of this product is good.
It is worth to purchase this product.
The features of this product are good.
I would recommend this product.

The Cronbach’s Alpha of the value scale for different sports products was as follows: alpha robe = .84, alpha hometrainer = .84, alpha handballs = .85 , alpha treadmill = .79.

Mean_Value1: Value perception of the first sports product: rope (t1).
Mean_Value2: Value perception of the second sports product: hometrainer (t2).
Mean_Value3: Value perception of the third sports product: handballs (t3).
Mean_Value4: Value perception of the last sports product: treadmill (t4).
Mean_Value1234: Value perception of all sports products: rope, hometrainer, handballs, treadmill.

All dependent variables were assessed on a 6-point-Likert-scale ranging from 1 =‘strongly disagree’ to 6 =‘strongly agree’.

Independent variables

condition: There were four different conditions. The participants received a brief description before evaluating each sports product regarding its effort and value. The description either contained two goals or one and the participants either got the sportgoal (for instance: building up muscles) or the alternativegoal first (for instance: minimizing stress).

condition == 1: two goals (sportgoal + alternativegoal)

condition == 2: two goals (alternativegoal + sportgoal)

condition == 3: one goal (sportgoal)

condition == 4: one goal (alternativegoal)
condition_betweenfactor1: This factor separated probands having one from those having two goals (unifinal vs. multifinal).

condition_betweenfactor1 == 1: one goal attached to the sports product

condition_betweenfactor1 == 2: two goals attached to the sports product
order_betweenfactor2: This factor separated probands getting the sportgoal first from those getting the alternativegoal first.

order_betweenfactor1 == 1: sportgoal first

order_betweenfactor1 == 2: alternativegoal first

Descriptive variables

case: Number for each person.
country: Residence of the probands with Switzerland = 1 and Germany = 2.
gender: Gender of the probands with male = 1 and female = 2.
age: Age of the probands (open question).

2. Questions

Question 1:

What are the characteristics of the analyzed sample? How many participants are in each condition? And are the dependent variables normally distributed?

Question 2:

Do the means of the unifinal vs. multifinal condition differ for the the value estimation of the treadmill?

Question 3:

Does the fact to receive one or two goals in the description of the different sports products or the age of the probands predict the estimation of their value?

Question 4:

Is there a relation between the constructs value and effort?

Question 5:

Do the means of the unifinal vs. multifinal condition differ for the effort estimation of the rope?

3. Analyses

Multifinality <- read.csv("~/Desktop/20150714_Multifinality _18variables2.csv", sep=";", dec=",", header = T, stringsAsFactors=FALSE)

3.1 Marking missing items

Multifinality[Multifinality == -9] <- NA

Multifinality$age.new <- Multifinality$age 
Multifinality$age.new [!(Multifinality$age.new %in% seq(10, 100, 1))] <- NA
Multifinality$age.new

##   [1] 22 23 24 25 24 24 54 22 26 22 50 58 23 22 54 24 48 23 20 27 22 23 24
##  [24] 21 21 23 24 21 30 22 27 21 22 25 24 24 62 24 35 45 43 53 47 54 56 48
##  [47] 20 21 24 24 23 53 20 24 48 22 23 28 25 21 21 22 24 25 22 21 22 23 63
##  [70] 39 23 21 21 24 38 65 24 22 45 57 60 22 23 24 53 23 21 23 23 65 24 43
##  [93] 24 56 24 24 23 20 19 23 23 23 24 54 23 24 24 23 22 24 24 46 23 52 47
## [116] 24 23 23 59 35 30 25 21 23 22 23 22 22 23 24 28 30 53 55 18 21 47 23
## [139] 22 23 24 23 27 57 24 23 24 24 30 22 19 42 25 23 24 23 19 23 22 24 24
## [162] 23 26 23 24 22 23 24 27 28 24 23 30 31 23 24 25 25 23 20 42 27 24 24
## [185] 24 24 23 21 28 21 52 29 17 21 19 23 23 24 22 24 23 24 28 22 22 21 25
## [208] 22 23 25 22 25 27 23 20 43 20 28 28 22 22 23 21 26 21 24

3.2 Question 1:

What are the characteristics of the analyzed sample? How many participants are in each

condition? And are the dependent variables normally distributed?

3.2.1 Characteristics of the analyzed sample

hist(x= Multifinality$age, main ="Graphic 1: Age Distribution", xlab= "Age in years", ylab= "Frequency", ylim=c(0,150))
abline(v= median(Multifinality$age), lwd=2, lty=2, col = "royalblue")
abline(v= mean(Multifinality$age), lwd=2, lty=2, col = "red")

legend("bottomright",
       legend = c("median age", "mean age"), 
       col = c("royalblue", "red"), 
       pch = c(16, 16)
       )

mean(Multifinality$age)

## [1] 28.32743

# The average proband's age was 28.33 years.
median(Multifinality$age.new, na.rm = TRUE)

## [1] 24

# The median of the probands' age was 24 years.
range(Multifinality$age.new)

## [1] 17 65

# The age range was between 17 and 65 years.
sd(Multifinality$age.new)

## [1] 11.217

# The standard deviation of the age of the probands was 11.22 years.
table(Multifinality$gender)

## 
##   1   2 
## 109 116

# 109 men and 116 women participated in the study, one proband made no statements concerning age.
sum(table(Multifinality$gender))

## [1] 225

# A total of 226 probands participated in the study.
(109.5*100)/226

## [1] 48.45133

# 48.45% of the participants were men.
(116.5*100)/226

## [1] 51.54867

# 51.55% of the participants were women
# 0.5 was added to each of the genders to deal with the one participant without gender indication.
table(Multifinality$country)

## 
##   1   2 
##  98 128

# 98 people from Switzerland und 128 from Germany participated in the study.

3.2.2 Distribution to the different conditions

table(Multifinality$condition)

## 
##  1  2  3  4 
## 54 59 62 51

# 54 probands were in the multifinal condition sportgoal-alternativegoal 
# 59 were in the multifinal condition alternativegoal-sportgoal  
# 62 probands were in the unifinal condition sportgoal
# 51 probands were in the unifinal condition alternativegoal 
table(Multifinality$condition_betweenfactor1)

## 
##   1   2 
## 113 113

# 50% of the proband only had one goal attached to the sports product
# 50% of the probands had two goals attached to the sports product 

table(Multifinality$order_betweenfactor2)

## 
##   1   2 
## 116 110

#  116 probands got the sportgoal first and 110 probands got the alternativegoal first.

3.2.3 Checking the construct and effort for normal distribution

shapiro.test(Multifinality$Mean_Effort1)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Effort1
## W = 0.9248, p-value = 2.557e-09

shapiro.test(Multifinality$Mean_Effort2)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Effort2
## W = 0.9566, p-value = 2.419e-06

shapiro.test(Multifinality$Mean_Effort3)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Effort3
## W = 0.9507, p-value = 5.75e-07

shapiro.test(Multifinality$Mean_Effort4)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Effort4
## W = 0.9257, p-value = 3.03e-09

# As all four tests returned p-values that were smaller than .05.
# We can assume that all the dependent variables of the construct effort are not normally distributed according to the Shapiro-Wilk-Test.

shapiro.test(Multifinality$Mean_Value1)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Value1
## W = 0.9672, p-value = 4.352e-05

shapiro.test(Multifinality$Mean_Value2)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Value2
## W = 0.9857, p-value = 0.02246

shapiro.test(Multifinality$Mean_Value3)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Value3
## W = 0.9857, p-value = 0.02305

shapiro.test(Multifinality$Mean_Value4)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Value4
## W = 0.9877, p-value = 0.0498

shapiro.test(Multifinality$Mean_Value1234)

## 
##  Shapiro-Wilk normality test
## 
## data:  Multifinality$Mean_Value1234
## W = 0.9814, p-value = 0.004472

# For value, all four tests returned p-values that were smaller than .05.
# We can thus assume that all the dependent variables of the construct value are neither normally distributed  according to the Shapiro-Wilk-Test. 
# Nevertheless, the p-values were a lot higher compared to the construct effort. 

boxplot(Multifinality$Mean_Value1234)

# The boxplots indicates some outliers for the construct value.

Conclusion question 1:

Within the range of the online study, 226 (M = 28.33, SD = 11.22 range: 17 to 65 years) participants evaluated four different sports products in regard to effort and value. 50% of the probands had two goals attached to the sports product and 50% of the proband only had one goal attached to the sports product.116 probands got the sportgoal first and 110 probands got the alternativegoal first. Neither the construct effort nor the construct value are normally distributed. In order to conduct the required analysis for this assignment, I am still going to use tests that require normal distribution. Therefore, the results have to be intrepreted with caution.

3.3 Question 2:

Do the means of the unifinal vs. multifinal condition differ for the value estimation of the treadmill?

aggregate(formula = Mean_Value4  ~ condition_betweenfactor1, 
          FUN= mean, 
          na.rm= T, 
          data= Multifinality)

##   condition_betweenfactor1 Mean_Value4
## 1                        1    3.750000
## 2                        2    3.743363

# Mean unifinal = 3.75, Mean multifinal = 3.74

# T-Test
test.result <- t.test(formula = Mean_Value4  ~ condition_betweenfactor1, 
                      data = Multifinality, 
                      alternative = "two.sided")
test.result

## 
##  Welch Two Sample t-test
## 
## data:  Mean_Value4 by condition_betweenfactor1
## t = 0.0461, df = 223.997, p-value = 0.9632
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.2768667  0.2901410
## sample estimates:
## mean in group 1 mean in group 2 
##        3.750000        3.743363

Conclusion question 2:

The t-test revealed that the value perception of the treadmill was not significantly different for the unfiinal (one goal) compared to the multifinal (two goals) condition (t(224) = 0.05, p = .9632, 95% CI =[- 0.28; 0.29], two-tailed test).

3.4 Question 3:

Does the fact to receive one or two goals in the description of the different sports products or the age of the probands predict the estimation of their value?

3.4.1 Conducting a regression with condition as independent variable and the mean fo all sports prodcuts as dependent variable.

# Regression
Mean_Value1234.lm <- lm(Mean_Value1234 ~ condition + age, 
                        data = Multifinality)
summary(Mean_Value1234.lm)

## 
## Call:
## lm(formula = Mean_Value1234 ~ condition + age, data = Multifinality)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.72459 -0.42463  0.04023  0.49015  2.00844 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.095880   0.183712  22.295   <2e-16 ***
## condition   -0.033025   0.048545  -0.680    0.497    
## age         -0.007099   0.004710  -1.507    0.133    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7917 on 223 degrees of freedom
## Multiple R-squared:  0.01253,    Adjusted R-squared:  0.00367 
## F-statistic: 1.414 on 2 and 223 DF,  p-value: 0.2453

3.4.2 Creating a plot for graphic illustration

par(mfrow= c(1, 2)) # in order to put both plots next to each other

one.goal <- subset(Multifinality, condition == 3)
two.goals <- subset(Multifinality, condition == 1)

# Create a blankplot
plot(x=1, y= 1, xlab= "Age", ylab = "Value Sports Products", type = "n", main = "Graphic 2: Relation between age, 
value & different conditions", xlim= c(0, 100), ylim = c(0, 6))
# Add red points for one goal and bluepoints for two goals
points(one.goal$age, one.goal$Mean_Value1234, pch= 16, col ="red")
points(two.goals$age,two.goals$Mean_Value1234, pch=16, col = "skyblue")

abline(lm(
       Multifinality$Mean_Value1234 ~ Multifinality$age)
       )

legend("bottomright",
       legend = c("one goal", "two goals"), 
       col = c("red", "skyblue"), 
       pch = c(16, 16)
       )
one.goal <- subset(Multifinality, condition == 4)
two.goals <- subset(Multifinality, condition == 2)

# create a blankplot
plot(x=1, y= 1, xlab= "Age" , ylab = "Value Sports Products", type = "n", main = "Graphic 3: Relation between age,
value & different conditions", xlim= c(0, 100), ylim = c(1, 6))

points(one.goal$age, one.goal$Mean_Value1234, pch= 16, col ="green")

points(two.goals$age,two.goals$Mean_Value1234, pch=16, col = "yellow")

abline(lm(
       Multifinality$Mean_Value1234 ~ Multifinality$age)
       ) 

legend("bottomright",
       legend = c("one goal", "two goals"), 
       col = c("green", "yellow"), 
       pch = c(16, 16)
       )

Conclusion question 3:

The dependent variable of value did not regress on the condition_betweenfactor1 (r= - 0.033, t(223) = - 0.86, p = .497) or the age (r= - 0.071, t(223) = - 1.51, p = .133. The results of the Omnibus-Test were F(2/223) = 1.414, p = .2453 R2(adjusted) = 0.0037. Therefore, one can draw the conclusion that the fact that to reveive one goal compared to two and the age aren’t good predictors for the value of the different sports products.

3.5. Question 4:

Is there a relation between the constructs value and effort?

  cor.test(Multifinality$Mean_Value1, Multifinality$Mean_Effort1)

## 
##  Pearson's product-moment correlation
## 
## data:  Multifinality$Mean_Value1 and Multifinality$Mean_Effort1
## t = 3.1352, df = 224, p-value = 0.001947
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.0765792 0.3267873
## sample estimates:
##       cor 
## 0.2050306

# Rope: positive correlation (r = .21, p = .002)
  
  cor.test(Multifinality$Mean_Value2, Multifinality$Mean_Effort2)

## 
##  Pearson's product-moment correlation
## 
## data:  Multifinality$Mean_Value2 and Multifinality$Mean_Effort2
## t = 3.0619, df = 224, p-value = 0.002468
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.07180928 0.32249649
## sample estimates:
##       cor 
## 0.2004314

# Hometrainer: positive correlation (r = .20, p = .002)
  
  cor.test(Multifinality$Mean_Value3, Multifinality$Mean_Effort3)

## 
##  Pearson's product-moment correlation
## 
## data:  Multifinality$Mean_Value3 and Multifinality$Mean_Effort3
## t = 4.9278, df = 224, p-value = 1.617e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1899895 0.4258563
## sample estimates:
##      cor 
## 0.312736

# Handballs: positive correlation (r = .31, p < .001)
  
  cor.test(Multifinality$Mean_Value4, Multifinality$Mean_Effort4)

## 
##  Pearson's product-moment correlation
## 
## data:  Multifinality$Mean_Value4 and Multifinality$Mean_Effort4
## t = 2.9107, df = 224, p-value = 0.003971
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.0619423 0.3135877
## sample estimates:
##       cor 
## 0.1908996

# Treadmill: positive correlation (r = .20, p = .004)

par(mfrow= c(2, 2))
  
  plot(x = Multifinality$Mean_Value1,
       y = Multifinality$Mean_Effort1,
       main = "Graphic 4: Correlation of Value and 
Effort rope",
       xlab = "Value rope",
       ylab = "Effort rope",
       xlim = c(0, 6), 
       ylim = c(0, 6), 
       col = gray(.5,.5),
       pch = 16,
       cex = 1, 
       type = "p")
  
abline(lm
       (Multifinality$Mean_Value1 ~ Multifinality$Mean_Effort1)
       )
  
  plot(x = Multifinality$Mean_Value2,
       y = Multifinality$Mean_Effort2,
       main = "Graphic 5: Correlation of Value and 
Effort hometrainer",
       xlab = "Value hometrainer",
       ylab = "Effort hometrainer",
       xlim = c(0, 6), 
       ylim = c(0, 6), 
       col = gray(.5,.5),
       pch = 16,
       cex = 1, 
       type = "p")
  
abline(lm
       (Multifinality$Mean_Value2 ~ Multifinality$Mean_Effort2)
       )
  
  plot(x = Multifinality$Mean_Value3,
       y = Multifinality$Mean_Effort3,
       main = "Graphic 6: Correlation of Value and 
Effort handballs",
       xlab = "Value handballs",
       ylab = "Effort handballs",
       xlim = c(0, 6), 
       ylim = c(0, 6), 
       col = gray(.5,.5),
       pch = 16,
       cex = 1, 
       type = "p")
 
abline(lm
       (Multifinality$Mean_Value3 ~ Multifinality$Mean_Effort3)
       )
  
  plot(x = Multifinality$Mean_Value4,
       y = Multifinality$Mean_Effort4,
       main = "Graphic 7: Correlation of Value and 
Effort treadmill",
       xlab = "Value treadmill",
       ylab = "Effort treamdill",
       xlim = c(0, 6), 
       ylim = c(0, 6), 
       col = gray(.5,.5),
       pch = 16,
       cex = 1, 
       type = "p")

abline(lm
       (Multifinality$Mean_Value4 ~ Multifinality$Mean_Effort4)
       )

Conclusion question 4:

The constructs effort and value correlate significantly (p < .01) for all four sports products.

3.6 Question 5:

Do the means of the unifinal vs. multifinal condition differ for the effort estimation of the rope?

# T-Test
test.result <- t.test(formula = Mean_Effort1 ~ condition_betweenfactor1,
                      data = Multifinality, 
                      alternative = "two.sided")
test.result

## 
##  Welch Two Sample t-test
## 
## data:  Mean_Effort1 by condition_betweenfactor1
## t = -0.9282, df = 219.794, p-value = 0.3543
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.3132415  0.1126516
## sample estimates:
## mean in group 1 mean in group 2 
##        4.890855        4.991150

Conclusion question 5:

The t-test revealed that the effort perception of the rope is not significantly different for the unifinal(one goal) compared to the multifinal (two goals) condition (t(220) = - 0.93, p = .3543, 95% CI =[- 0.31; 0.11], two-tailed test).

3.7 Creating a custom function to write

multifinality.custom.function <- function(x, what) {
if (what == "sum") {output <- sum(x)}
if (what == "mean") {output <- mean(x)}
if (what == "done") {output <- "I am done with analyzing, I can start writing the conclusion" }

return(output) 

}
multifinality.custom.function(x= c(1, 2, 3, 4, 5), what = "done")

## [1] "I am done with analyzing, I can start writing the conclusion"

4. Conclusion

conclusion.custom.function <- function(a, b, c)  
  { 

paste("The purpose of this research study was to",a, "to which extent the", b, "when given different ones with regards to content, influence perceived", c,"to achieve said goals.")  }

conclusion.custom.function ("clarify","number of goals", "value and effort")

## [1] "The purpose of this research study was to clarify to which extent the number of goals when given different ones with regards to content, influence perceived value and effort to achieve said goals."

Within the range of the online study, 226 (M = 28.33, SD = 11.22 range: 17 to 65 years) participants evaluated four different sports products in regard to effort and value. 50% of the probands had two goals attached to the sports product and 50% of the proband only had one goal attached to the sports product. The multifinal condition, in which the probands received two goals, was expected to evaluate the four sports products as more strenous and more precious.

Contradictory to expectations, a t-test showed that the value perception of the treadmill was not different between the unifinal and the multifinal condition (t(224) = 0.05, p = .9632, 95% CI =[- 0.28; 0.29], two-tailed test). Moreover, an additional t-test revealed that the effort perception of the rope was not significantly different for the unifinal compared to multifinal condition (t(220) = - 0.93, p = .3543, 95% CI =[- 0.31; 0.11], two-tailed test). Additionally, the value perception was not influenced by the condition or the age of the probands.

Finally, the findings of this study showed strong evidence that there is a positive relation between the perception of value and effort as the construct value and effort correlated positiviely for each of the products (Graphic 4-7).This goes in line with the effort-heuristic which assumes that people use effort as a heuristic in order estimate the value of products (Koo & Fisbach, 2010).

Literature:

Koo, M., & Fishbach, A. (2010). A silver lining of standing in line: Queuing increases value of products. Journal of marketing research, 47(4), 713-724. doi: 10.1509/jmkr.47.4.713

Data Analysis and visualization in R

Zoe Jonassen

Juli 2015

Project: “Multifinality”

1. Dataset description

1.1 How did you obtain the dataset?

1.2 How were the data originally collected?

1.3 How many rows and columns are in the dataset?

1.4 What are the columns in the dataset? For each column, give the variable name and a brief description of what it represents.

Dependent variables

Effort Scale:

Value Scale:

Independent variables

Descriptive variables

2. Questions

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

3. Analyses

3.1 Marking missing items

3.2 Question 1:

What are the characteristics of the analyzed sample? How many participants are in each

condition? And are the dependent variables normally distributed?

3.2.1 Characteristics of the analyzed sample

3.2.2 Distribution to the different conditions

3.2.3 Checking the construct and effort for normal distribution

Conclusion question 1:

3.3 Question 2:

Do the means of the unifinal vs. multifinal condition differ for the value estimation of the treadmill?

Conclusion question 2:

3.4 Question 3:

Does the fact to receive one or two goals in the description of the different sports products or the age of the probands predict the estimation of their value?

3.4.1 Conducting a regression with condition as independent variable and the mean fo all sports prodcuts as dependent variable.

3.4.2 Creating a plot for graphic illustration

Conclusion question 3:

3.5. Question 4:

Is there a relation between the constructs value and effort?

Conclusion question 4:

3.6 Question 5:

Conclusion question 5:

3.7 Creating a custom function to write

4. Conclusion

Literature: