Sleep Deprivation as Shown in the Variable

¶ … Sleep Deprivation

As shown in the variable table, the two relevant variables for determining how sleep affects abilities are Hours (the number of hours each participant has gone without sleep) and Errors (the number of errors each participant made in their arithmetic test). Both are quantitative variables; Hours is the independent variable in this study, and Errors is the dependent variable. This particular study has a sample size of ten -- ten subjects were examined during the course of the research. Analysis of the raw data collected from these subjects was conducted using the spreadsheet and statistical program Microsoft Excel.

By highlighting the two columns of relevant data and using Excel's built-in functions, a scatter plot was created. The arrangement of the data in the plot visually suggests a linear relationship, which makes further regression analysis appropriate. Excel was thus used to add a trendline to the scatter plot, and to display the equation that fits this line. The line closely matches the raw data points in the scatter plot, with few data points very far from the line and the general trend closely followed. The regression equation is y=0.475x+3, where y is the number of errors (the dependent variable) and x is the number of hours each participant went without sleep (the independent variable). The coefficient of x shows a relatively gradual increase in the number of errors as the number of hours without sleep increases. Using this equation, the number of errors that would be expected after 10 hours without sleep is 0.475(10)+3=7.75 or about 8 errors. At 4 hours without sleep, there would be 0.475(4)+3=4.9 or about 5 errors. A greater variance in x range than y range would likely indicate a curved relationship if any. The strength of the relationship between hours without sleep and errors on the test, as can be seen from the correlation coefficient, is quite high).

Cheese, Please!

For this study, as can be seen in the variable table, Sodium (the amount of sodium per slice of each brand of cheese) and Calories (the number of calories per slice of each brand of cheese), are the two relevant variables, both of which are quantitative variables. As there were five brands of cheese studied in this research, the sample size is five, and the way in which the question in this research is posed, the amount of sodium (i.e. Sodium) is the independent variable and the amount of calories (i.e. Calories) is the dependent variable. Again, preliminary statistical analysis was carried out on the raw data using Microsoft Excel.

The scatter plot created via Excel does not suggest a relationship between the variables. Though there is a cluster containing most of the data points and one variable that varies significantly in terms of both calories and sodium, there is not enough of a range in the data (and possibly not enough data) to suggest any relationship. Further analysis is not really necessary, as a cursory examination of the plot shows that there is not enough data to form a conclusion. Further analysis might even lead to some confusion, as calculating the correlation coefficient using Excel's CORREL function has a result of 0.98, suggesting a very strong correlation in a standard data set with a strong trendline and a range of distributions. In this instance, however, the correlation coefficient is only reaffirming that most of the data points are very tightly clustered around one spot -- at approx. 300mg sodium and 30 calories per slice of cheese. Reading an actual correlation between the two identified variables would be foolish in this instance when the selection sample is small, the range incredibly narrow, and a host of other variables (i.e. other ingredients in the cheeses/differences in the recipes) have been ignored.