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A researcher investigated whether there was a relationship between the time spent being read to as a child (at age 3) and later performance on a second-grade English skills The parental report of the amount of time spent reading to their child (on a 1 to 10 scale) and the scores on an English skills exam (on a 10 to 50 scale) were recorded for 30 students (higher scores indicate being read to more at age 3 and better performance on the exam in second grade, respectively).
 
1) State the null and alternative hypothesis.
2) State a research question for the data.
3) Calculate the correlation coefficient between the two variables in SPSS. What is the value of the correlation?
4) Is the correlation significant? Test at α = .05.
5) What is the effect size for the study? Would you characterize the effect size as small, medium, or large?
6) Write the results of the study using APA format as appropriate.

Let's go through the analysis process based on the information provided.

### 1. Null and Alternative Hypotheses

- **Null Hypothesis (H₀)**: There is no relationship between the time spent being read to as a child (at age 3) and performance on the second-grade English skills exam.
- **Alternative Hypothesis (H₁)**: There is a positive relationship between the time spent being read to as a child (at age 3) and performance on the second-grade English skills exam.

### 2. Research Question

- **Research Question**: Does the amount of time spent being read to at age 3 predict later performance on a second-grade English skills exam?

### 3. Correlation Coefficient Calculation in SPSS

To find the correlation coefficient between "reading time" and "exam scores" in SPSS, you would follow these steps:

   - Open the dataset in SPSS.
   - Click on **Analyze > Correlate > Bivariate**.
   - Select **readingtime** and **examscores** as the variables.
   - Check the **Pearson** correlation option and **flag significant correlations**.
   - Set the **two-tailed** test option.

The output will display the **Pearson correlation coefficient (r)**, which represents the strength and direction of the relationship between reading time and exam scores.

### 4. Significance Test

With a correlation test at a significance level of α = .05, you will compare the **p-value** obtained from the SPSS output:

- If **p < 0.05**, the correlation is statistically significant, meaning we can reject the null hypothesis.
- If **p ≥ 0.05**, the correlation is not statistically significant, meaning we fail to reject the null hypothesis.

### 5. Effect Size

The correlation coefficient (r) itself serves as a measure of effect size in this context:

- **Effect size interpretations for r**:
  - Small effect: \( r = 0.1 \) to \( 0.3 \)
  - Medium effect: \( r = 0.3 \) to \( 0.5 \)
  - Large effect: \( r > 0.5 \)

After obtaining the correlation value, we can classify the effect size based on these guidelines.

### 6. Results in APA Format

Assuming you find a significant positive correlation, you can write the results as follows:

- **Example APA format**: "A Pearson correlation analysis indicated a significant positive relationship between the time spent being read to at age 3 and second-grade English skills scores, \( r(N = 30) = [correlation value], p = [p-value] \). The effect size was [small/medium/large] based on the correlation value."

Would you like assistance in calculating these steps further or need clarification on any specific part? Here are some follow-up questions that might guide additional analysis:

1. How can we interpret the direction and strength of the relationship if the correlation coefficient is close to 0?
2. What alternative tests could we use if the data were not normally distributed?
3. How would a non-significant result affect the interpretation of this study?
4. Could the findings vary with a different sample size or age range?
5. How could confounding variables (like socioeconomic status) influence the correlation?

**Tip**: Always ensure data assumptions (like linearity and normality) before running a Pearson correlation to improve accuracy in interpretation.

A researcher investigated whether there was a relationship between the time spent being read to as a child (at age 3) and later performance on a second-grade English skills exam. The parental report of the amount of time spent reading to their child (on a 1 to 10 scale) and the scores on an English skills exam (on a 10 to 50 scale) were recorded for 30 students (higher scores indicate being read to more at age 3 and better performance on the exam in second grade, respectively).

1) State the null and alternative hypothesis.
2) State a research question for the data.
3) Calculate the correlation coefficient between the two variables in SPSS. What is the value of the correlation?
4) Is the correlation significant? Test at α = .05.
5) What is the effect size for the study? Would you characterize the effect size as small, medium, or large?
6) Write the results of the study using APA format as appropriate.

Explore a study investigating the correlation between time spent being read to at age 3 and second-grade English skills. This analysis involves hypothesis testing, correlation calculation, and effect size interpretation. Learn how to calculate and interpret correlation significance at α = .05 using SPSS.

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