Describe the strength of the relationship (e.g. very strong, moderate, weak, etc.).
Study Description: A school educator is interested in determining the relationships between grade point average (GPA) and IQ scores among ninth graders. The educator takes a random sample of 40 ninth graders aged 14 years old and administers the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV). The WISC-IV includes a Full Scale IQ (FSIQ; however for this assignment we will just call it IQ) that comprises verbal comprehension, perceptual reasoning, working memory, and processing speed skills.
Output file: See Week_2_SPSS_Output.pdf
.
Answer the following Questions:
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Order Paper Now- Hypothesis – Formulate a hypothesis about the two variables. What do you think is the relationship between IQ scores and GPA?
- Variables – Identify the variables and each of their attributes: discrete or continuous, quantitative or categorical, scale of measurement (nominal, ordinal, interval, or ratio), and independent or dependent.
- Descriptive statistics – Write an overview of the descriptive statistics (at least two paragraphs), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Include the following in your discussion:
- How do the measures of central tendency and variability provide us with an overview of the characteristics and shape of the distribution of each variable? What are these statistic
- Keeping in mind that the WISC-IV has a mean of 100 and Standard Deviation of 15, what assumptions could you make about the IQ scores and suitability of this IQ test for the group of students sampled?
- Keeping in mind that the WISC-IV has a mean of 100 and Standard Deviation of 15, how many students’ IQ scores in this sample are within one standard deviation below the test’s mean? Two standard deviations below the test’s mean? What percentage of students in this sample had an IQ score less than or equal to 70? An IQ score greater or equal to 100?
- Correlation – Write an overview of the results of the correlation (at least two paragraphs), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Consider the following in your overview and conclusions:
- Is there a significant correlation between IQ scores and GPA? If so, what does a significant correlation mean?
- Using the correlation table and scatterplot, explain whether the relationship is positive, negative, or no correlation.
- Describe the strength of the relationship (e.g. very strong, moderate, weak, etc.).
- What do the results tell us about our hypotheses?
- What conclusions can we draw from these results? What conclusions can we NOT make using these results?
- What issues regarding the sample used or how the data was collected should be considered in the interpretation of the data?
- Regression – Write an overview of the results of the regression (1 paragraph), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Consider the following in your overview and conclusions:
- In the regression, what variable is the dependent variable and what variable is the independent variable?
- What do the regression results tell us about IQ scores and GPA?
FREQUENCIES VARIABLES=IQ GPA
/STATISTICS=STDDEV VARIANCE RANGE MEAN MEDIAN MODE SKEWNESS SESKEW
/HISTOGRAM
/ORDER=ANALYSIS.
Frequencies
Statistics
IQ GPA
N Valid 40 40
Missing 0 0
Mean 85.1000 2.7300
Median 82.0000 2.8500
Mode 66.00 a 2.90
Std. Deviation 16.40169 .64815
Variance 269.015 .420
Skewness .374 .012
Std. Error of Skewness .374 .374
Range 52.00 2.20
a. Multiple modes exist. The smallest value is shown
Frequency Table
IQ
Frequency Percent Valid Percent
Cumulative
Percent
Valid 62.00 2 5.0 5.0 5.0
66.00 3 7.5 7.5 12.5
67.00 2 5.0 5.0 17.5
70.00 2 5.0 5.0 22.5
71.00 3 7.5 7.5 30.0
74.00 3 7.5 7.5 37.5
76.00 3 7.5 7.5 45.0
82.00 3 7.5 7.5 52.5
84.00 1 2.5 2.5 55.0
88.00 3 7.5 7.5 62.5
89.00 1 2.5 2.5 65.0
92.00 1 2.5 2.5 67.5
94.00 1 2.5 2.5 70.0
97.00 1 2.5 2.5 72.5
98.00 2 5.0 5.0 77.5
103.00 1 2.5 2.5 80.0
107.00 2 5.0 5.0 85.0
108.00 1 2.5 2.5 87.5
109.00 1 2.5 2.5 90.0
110.00 1 2.5 2.5 92.5
112.00 1 2.5 2.5 95.0
113.00 1 2.5 2.5 97.5
114.00 1 2.5 2.5 100.0
Total 40 100.0 100.0
GPA
Frequency Percent Valid Percent
Cumulative
Percent
Valid 1.70 2 5.0 5.0 5.0
1.80 2 5.0 5.0 10.0
1.90 2 5.0 5.0 15.0
2.00 4 10.0 10.0 25.0
2.10 1 2.5 2.5 27.5
2.20 1 2.5 2.5 30.0
2.40 2 5.0 5.0 35.0
2.50 2 5.0 5.0 40.0
2.60 1 2.5 2.5 42.5
2.80 3 7.5 7.5 50.0
2.90 6 15.0 15.0 65.0
3.00 1 2.5 2.5 67.5
3.10 2 5.0 5.0 72.5
3.20 1 2.5 2.5 75.0
3.30 3 7.5 7.5 82.5
3.40 1 2.5 2.5 85.0
3.50 2 5.0 5.0 90.0
3.60 1 2.5 2.5 92.5
3.80 1 2.5 2.5 95.0
3.90 2 5.0 5.0 100.0
Total 40 100.0 100.0
Histogram
CORRELATIONS
/VARIABLES=IQ GPA
/PRINT=TWOTAIL NOSIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE.
Correlations
Descriptive Statistics
Mean Std. Deviation N
IQ 85.1000 16.40169 40
GPA 2.7300 .64815 40
Correlations
IQ GPA
IQ Pearson Correlation 1 .608 **
Sig. (2-tailed) .000
N 40 40
GPA Pearson Correlation .608 ** 1
Sig. (2-tailed) .000
N 40 40
**. Correlation is significant at the 0.01 level (2-tailed).
Scatterplot
REGRESSION
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT GPA
/METHOD=ENTER IQ
/RESIDUALS HISTOGRAM(ZRESID) NORMPROB(ZRESID).
Regression
Variables Entered/Removed b
Model Variables
Entered
Variables
Removed Method
d
i
m
e
n
s
i
o
n
0
1 IQ a . Enter
a. All requested variables entered.
b. Dependent Variable: GPA
Model Summary b
Model
R R Square
Adjusted R
Square
Std. Error of the
Estimate
d
i
m
e
n
s
i
o
n
0
1 .608 a .370 .353 .52132
a. Predictors: (Constant), IQ
b. Dependent Variable: GPA
ANOVA b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.057 1 6.057 22.286 .000 a
Residual 10.327 38 .272
Total 16.384 39
a. Predictors: (Constant), IQ
b. Dependent Variable: GPA
Coefficients a
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .685 .441 1.554 .128
IQ .024 .005 .608 4.721 .000
a. Dependent Variable: GPA
Residuals Statistics a
Minimum Maximum Mean Std. Deviation N
Predicted Value 2.1750 3.4244 2.7300 .39408 40
Residual -1.33995 1.50878 .00000 .51459 40
Std. Predicted Value -1.408 1.762 .000 1.000 40
Std. Residual -2.570 2.894 .000 .987 40
a. Dependent Variable: GPA
Charts
