# Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psycho

Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). Toe researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient $$\displaystyle{\left(\text{measured on a 7-point scale where}\ {1}=\ \text{"not at all" and}\ {7}=\ \text{to a great extent"}\right)}.$$ Participants for the study were those who used a popular Web site for engaged couples. The Web site's directory was searched for those with "average" American names (e.g., "John Smith," "Sara Jones"). These individuals were then invited to participate in an online survey in exchange for a \$10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents. a) Identify the experimental units for this study. b) What are the variables of interest? Are they quantitative or qualitative in nature? c) Describe the population of interest. d) Do you believe the sample of 33 respondents is representative of the population? Explain. e. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. Toe participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.

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a) The experimental units are people who use that popular Web site for engaged couples, since those are the individuals from which we want some information (engagement ring price and level of appreciation). b) The variables measured were Engagement ring price and Level of appreciation The first variable (engagement ring price) is a quantitative variable, sinceit is a numerical measurement (in dollars). The second variable (level of appreciation) is qualitative, since it takes on values which are category names (integers ranging from 1 to7). Don't be tempted to think that this is a quantitative variable simply because it's values are numbers - the numbers are merely symbols (or codes) for categories ranging from "not at all appreciated" to "appreciated to a great extent". c) The population of interest consist of all people who use that popular Web site for engaged couples, since that's the collection of all individuals from which some information (engagement ring price and level of appreciation) is wanted. d) Yes, this sample is most likely representative. The sample included 33 people who usually visit that Web site. The participants were recruited based on their names (the researchers for those with "average" names). There is no reason that people with "average" names would differ, in any way, from the entire population, since name is not a characteristic that would determine someone's behaviour or tendencies. e) If available, you can use statistical sofware R to generate this random assignment (that's what we used, and we present the code below). Other optionsinclude Exel, Minitab or some websites. First we label each of the 50 participants in our random sample with numbers (integers) from 1 to 50. Then it,s sufficient to randomly choose 25 values from our set of 50 numbers (i.e. from our sample of 50 participants) and assingthem to play the role of gift-receiver (for instance). The remaining 25 people would then play the role of gift-giver. The following short piece of code written in statistical software R will perform the above procedure: $$\text{partipants}\leftarrow1:50\quad \#\# \text{random sample of 50 partipants}\\ \#\# \text{chose 25 random values from the above set of 50 values:}\\ \text{gift_givers}\leftarrow\text{sample (participants, 25, replace=F, prob=NULL)}\\ \text{gift_receivers}\leftarrow\text{setdiff(participants, gift_givers)}$$

For instance, we obtained the following result (assignment):

$$\begin{array}{c|c} \text{gift_giver} & \text{gift_receiver} \\ \hline 2 & 1 \\ 3 & 4 \\ 7 & 5 \\ 8 & 6 \\ 10 & 9 \\ 12 & 11 \\ 17 & 13 \\ 18 & 14 \\ 22 & 15 \\ 23 & 16 \\ 26 & 19 \\ 27 & 20 \\ 30 & 21 \\ 32 & 24 \\ 34 & 25 \\ 35 & 28 \\ 36 & 29 \\ 37 & 31 \\ 38 & 33 \\ 39 & 40 \\ 41 & 42 \\ 44 & 43 \\ 46 & 45 \\ 47 & 49 \\ 48 & 50\\ \end{array}$$