Does a bigger brain make you smarter?
i. An Introduction (< 1 page) containing background information and the goal of the report. Find the information online and elsewhere and write a brief summary of the study and what the variables and data are about, so as to give some context to your report. (5 Marks; -1/2 SPSS ref; emphasize variable explanation)
ii. An Analysis section containing all observations and of the analysis required in the report, and any that helps to support the goal of the report. This section should only contain statistical analysis, and no interpretation. Include subsections (Summary/Descriptive Statistics, Graphic Methods, Linear/Regression Analysis, and Hypothesis Testing, Population Estimation).
a. Perform any appropriate descriptive statistics and graphical methods. Use graph styles presented in class and labs to produce graphs and look at the distribution of PIQ and MRI c unt before and after splitting genders. Can you see any connection with and without gender as a factor? Are there any trends or patterns? Can you see anything worth questioning or studying about the data? Summarize the basic statistics in terms of location and dispersion, and distribution of PIQ and MRI Count and also compare the differences between males and females in both.
b. If appropriate, plot scatterplot or diagram and draw a regression line and compute its equation. Interpret any correlation and compute correlation coefficient and coefficient of determination relating the variables of interest. Can we make any predictions? Perform a linear regression to predict PIQ scores based on the MRI Count (brain size). Is there a significant relationship? Is there a significant relationship within each gender? Is brain size a good predictor of IQ in general and/or within each gender?
c. Include any hypothesis testing and population/variance estimation here as well. According to the Flynn Effect, IQ should rise over time (TED VIDEO - Why Our IQ Levels Are Higher than Our Grandparents). Since this study was in 1991 we would expect the mean IQ to be above the baseline 100. At the 5% level are the PIQ scores significantly above the 100 point baseline? (i.e., test value of 100, one-sided). Include all steps of the hypothesis testing process. Estimate an interval for the mean PIQ at the 95% confidence level, for each gender. Since the study was conducted in 1991, and according to the Flynn Effect the IQ should rise 3 points per decade (THE FLYNN EFFECT (Scientific American) does this interval help to confirm this? Include the intervals with proper interpretations as well. Test =118.3 and compare male vs. female for IQ. Also compare MRI for gender.
iii. Results, summarizing and giving context to the analysis. Interpretation and explanation of the results.
iv. Discussion and Conclusion(s), stating important or novel findings, comparison to other data available in the literature, and stating any future directions for further studies. Here you should write a short report (< 1 page) to summarize all your findings and conclusively answer whether there is a difference in IQ between males and females, and whether you can predict IQ by knowing the size of someone's brain. (Find the mean PIQ value for this sample by SPSS. What is the point estimate for the mean PIQ value of the population?
(2) Construct a 95% confidence level for the population mean by SPSS. Interpret the meaning of the interval in your own words. Based on the interval is it likely the PIQ average is associated with a larger brain size based on MRI values?
(3) Construct an 80% confidence level for the population mean by SPSS.
(4) How does the 80% confidence interval compare to the 95% interval?
(5) Perform a Hypothesis Test
a. State the null and alternative hypotheses.
b. Perform One-Sample or Two-Sample Test by SPSS and state significance or p-value.
c. Write your conclusion.
i. Do these data allow us to infer at the 5% significance level that IQ (intelligence) is related to brain size?
ii. Is it significantly more than the baseline 100? The population =118.3?
iii. Why does the 95% Confidence interval, and 5% test not give the same answer always?