**Statistics Thinking Activity**

# Student Learning Outcomes

- Differentiate between descriptive statistics and inferential statistics
- Differentiate between inferential test statistics an p-values
- Given a p-value make a decision about whether one should reject or retain the null hypothesis
- Given information about data decide which test one should use
- Given the descriptive statistics, a test statistic, and the p-value explain the findings using plain language, and in APA style.
- Choose the best interpretation of the data given inferential and descriptive statistics
- Select the appropriate conclusion given inferential statistics, means, and SDs

## A**pplication Activity 1**

Part A. Below are excerpts from journal articles. For each excerpt, identify the descriptive statistic and identify the inferential statistic. Also, decide which value is the test statistic and which value is the p-value. Then, decide what decision the author should make about the null and alternative hypothesis. Finally, based on the finding describe two possible interpretations of the data (see page. 178 in Mitchell et al. for help with this).

- Participants in the wronging condition reported a higher mean entitlement score (
*M*= 4.34,*SD*= 1.23) than did control participants (*M*= 3.85,*SD*= 1.19),*t*(92) = 1.96,*p*= .05. - Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations of the data?

- People who wrote about a time when their lives were unfair were more frustrated (
*M*= 2.45,*SD*= 1.21) than were people who wrote about a time when they were bored (*M*= 1.94,*SD*= 1.11),*t*(103) = 2.25,*p*= .03.- Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations?

- People who wrote about a time when their lives were unfair did report being more angry after writing the essay (
*M*= 2.05,*SD*= 1.18) than did people who wrote about a time when they were bored (*M*= 1.34,*SD*= .77),*t*(103) = 3.64,*p*< .001 - Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations?

- There was not a significant difference in the mean of the negative affect words on the PANAS between participants in the wronging condition (
*M*= 1.70,*SD*= .54) and control condition (*M*= 1.55,*SD*= .53),*t*(103) = 1.50,*p*= .14.- Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations?

- There was a strong positive relationships between eating ice cream and donation behavior,
*r*(56) = 0.78,*p*< .003. - Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations?

- Further, the ice cream eating was not related to massaging one’s forehead,
*r*(56) = 0.24,*p*= .15. - Bold descriptive statistics and underline or highlight inferential statistics.
- List test statistic _______________,
*p*value ________________ - What decision should the author make about the null hypothesis (i.e., retain or reject)?
- What are two possible interpretations?

- Is there a general pattern that you noticed across all results excerpts?

Part B. Choose the best interpretation of the data below.

Imagine I found the following correlation between attractiveness and life success, *r*(34) = 0.78, *p *= .003. Which of the following is the best interpretation of the data?

- Attractive people are less successful on average than unattractive people
- Attractive people are more successful on average compared to unattractive people
- There is a strong relationship between attractiveness and life success such that as attractiveness increases so does life success
- There is a weak relationship between attractiveness and life success such that as attractiveness increases so does life success
- There is a strong negative relationship between attractiveness and life success.

Imagine that I had two drugs, X and Z. I administered the drugs to people with sleep difficulties for one month. The mean amount of sleep difficulties reported in the drug X groupin the past month was 3.44 (*SD* = 2.34) and the mean in drug Z was 4.66 (*SD* = 1.23), *t*(56) = 2.10, *p *= .10. What is the best interpretation of the data?

- Drug Z decreased the frequency of sleep trouble as compared to Drug X
- There were no differences in sleep troubles reported by those in drug X group compared to those in the drug Z group.
- There was no significant relationship between drug type and reported sleep trouble
- There was a significant decrease in sleep troubles reported by those who consumed drug X compared to drug Z.
- Sleep trouble decreased as a function of drug use.

**Application Activity 2**

Imagine that I was interested in the effect of benevolent intentions on pleasure. Participants received one of two types of goodies: a tootsie roll with a note that read, “I picked this goodie just for you. I hope you like it!” or a note that read, “I was told to pick this goodie. So, whatever.” After the participants completed a puzzle and ate the candy they were asked how delicious they thought the good was on a scale that ranged from 1 (*not at all delicious*) to 6 (*extremely delicious*). The data are below.

Benevolent condition, *M *= 4.55, *SD* = 2.10 Apathetic condition, *M *= 2. 30 *SD* = 1.25

- Describe the mean differences in plain language.

- Describe the variability in both conditions.

- Decide which statistical test you should use.

- Imagine the following data:
*t*(38) = 6.38,*p*< .001. What would you conclude about the effect of benevolent intention on pleasure?

- Which of the above is an inferential statistic?

- Write an APA style sentence describing the descriptive and inferential statistics.

**Application Activity 3**

Imagine a researcher conducted a study using survey/correlation methods. She asked people complete the Happiness Scale and she asked how often they go on vacation. Then she correlated happiness and vacation frequency to see if there was a relationship. Finally, she divided people into four groups based on their income and examined the relationships separately.

Poor folks Moderate income folks Rich folks Filthy Rich folks

*r*(34) = .62 *r*(36) = .59 *r*(24) = .44 *r*(20) = .30

1)Describe the relationship between vacation frequency and happiness for rich folks.

2)In which group is the relationship between vacation frequency and happiness strongest?

3)What is the best interpretation of the data for moderate income folks?

4)Which of the following would support your above conclusion?

*r*(36) = .59,*p*= .06*r*(36) = .59,*p*= .08*r*(36) = .59,*p*= .05*r*(36) = .59,*p*= .16

5)Below are the actual data for moderate income folks. Given the data write an APA style sentence.

*r *= .56

df = 32

*p*< .001