Question

For the following situations, indicate the statistical test you would conduct and WHY (that is, explain the variables)!

choose between paired sample t test, one way anova test, 2 sample t test.

A researcher is interested in how consumers make purchase decisions for a specific type of product. He develops a survey where, among other things, he asks to what extent price matters to people (on a Likert scale from 1 to 5) and to what extent quality matters to people (on a Likert scale from 1 to 5) when they try to decide which brand to buy.

Respondents in a survey of 1,000 households were asked about their travel history. Specifically, they were asked how often they have been to Europe in the past five years (using a ratio scale). People were also classified by interest type (art-lovers, food-lovers, or sports-lovers). The question is whether interest type influences travel history.

A restaurant is working on a new strategy to get consumers to eat healthier. They decide to run an experiment. As part of the experiment, the restaurant varies the presentation format of their menu. One week, they present their menu in picture format (that is, patrons see the picture of a dish and the name). The other week, they present their menu in text format (that is, patrons see a text description of a dish and the name). The restaurant is measuring how much money customers spent (using a ratio scale) on a healthy meal each week.

Answer 1

1) paired sample t - test.

Researcher wants to test whether choices of people are based on price and quality equally or they are biased towards either factor . That is he is testing hypothesis that people are giving equal weightage to price and quality against alternative Hypothesis people prefer quality over price or price over quality ( either) . Here he is recording scores for both factor on same subject . A person who has rated quality is also going to rate price. So data for two factors is collected on same sample point . Therefore values are dependent and hence paired sample t test will be used. Here we are testing mean rating . t test is used to test difference in means.

Dependent Variable is likert scale rating which is based on two factors quality and price .

Note : sample would have been independent if say for observation 1 if person A is rating for quality and person B is rating for price . But here in the given example it's the Person A who rates quality as well as price . So if there are 10 observations , 10 people have rated . But for independent samples with 10 observations each 20 people are rating .

2) One way ANOVA

When we want to compare means of more than two groups we use ANOVA. Researcher is interested in checking if travel history ( number of times person have been to Europe in last 5 years) is differing across his interests . There are three groups being compared and travel history depends on one factor ( interests) therefore One way ANOVA is used. Dependent Variable is number of times person travelled to Europe in past 5 years And independent is interest .

3) two sample t test .

Restaurant owner wants to know what factor is influencing people more . Is it menu in picture format or menu in text format . He is testing if mean spending differs across two factors or it is same . Dependent Variable is money that people wish to spend based on two factors , picture format and text format menu . Samples are independent .