An independent variable is the variable that the experimenter manipulates in a formal experiment. An independent variable does not change when another variable changes. For example, an independent variable in an experiment could be a subject’s age. Other factors such as how much food the subject consume, how much they sleep, or work out will not change the subject’s age. A dependent variable is the variable that is measured in a formal experiment. The dependent variable depends on the manipulation of the independent variable in the experiment. For example, a dependent variable in an experiment could be a test score. The test score will change dependent on how much the subject studies, how much the subject sleeps the night prior to the test, or how much food the subject consumed prior to the test.

The nominal scale of measurement identifies a value into a descriptive category. However, the value does not have a numerical value. An example of a nominal scale measurement is gender, male or female. The ordinal scale of measurement identifies both a description and level. For instance, an ordinal scale of measurement can be used in a dog race. The category being measured is via a dog race and the level is determined by first, second, or third place. An interval scale of measurement looks at description, level, and equal distances. For example, Fahrenheit or Celsius temperature scales. The measurement of temperature increases in equal distances, or intervals. The ratio scale of measurement identifies description, level, equal distances, and at least a value of zero. An example of a ratio scale would be a scale measuring weight. When measuring weight on a scale, there is a description (obese or not obese), level (how much lost or gained), distance (units are equal to one another), and minimum value of zero.

The normal distribution is shaped like a bell and travels in both directions. The normal distribution varies in different sizes dependent on the mean and standard deviation. A normal distribution curves can be flat, spread out, or tall and skinny. The normal distribution is centered on the mean and the curve is symmetrical around the mean. The mean equals the median. The first standard deviation contains 68%, or two 34% sections, of the data. The second deviation contains 27%, or two 13.5% sections, of the data. The third deviation contains 4.7%, or two 2.35% section s, of the data. The fourth deviation contains 0.3%, or two .15% sections, of the data.

A Z-test takes two sets of data and compares both the sample and population to see if there is a significant difference. The z measure is found by subtracting the mean sample and population mean, then dividing it by the standard error of the mean. To find the standard error of the mean, divide the population standard deviation by the square root of the sample size. Once the z-value can be looked up on a z-table, if the z-value is negative it is below the population mean and will not show up on the z-table. Z-tests are typically used with standardized tests to see if the scores during a certain test session fall within or outside of the standard test performance.

A single sample t-test is typically used when an experiment is testing a certain population within a larger sample size, but the full population size’s information is not available. This type of sample test validates the sample mean of a certain population. The hypothesis formed in this type of test looks at if the average mean of the sample size matches with the mean of the population the sample is hypothesized to originate from. The assumptions made under a single sample t-test is that it is a random sampling, an interval or ratio scales of measurement, and the population must be normally distributed.

The main criterion when deciding between a Z-test and a single sample T-test starts with the sample size. A Z-test handles population sizes that have a quantity of 30 or more. A t-test handles smaller populations with a quantity of 30 or less. The Z-test follows a statistical hypothesis that falls in a normal distribution and the t-test follows data found by the experimenter. The t-test is more adaptable to non-standard experiments as the z-test requires certain criteria before it can used. For instance, z-tests are more preferred when the standard deviation is known. With that said, T-tests are typically used more.

An independent measure t-test is typically used when values from two separate samples are being compared and the values do not come matched in a pair. The group samples are independent and only take one test. The t-value can be found by dividing the difference between to the group means by the standard error from the difference between group means. Once the t-value is achieved, it can be looked up in the t-test table to determine a significant difference between the two sets of values. This will determine the efficacy of an experiment.

A repeated measure, dependent measure, t-test is used when there is a significant difference between populations and the values are dependent on one another. The hypothesis tested determines whether the difference between the values in the experiment belong to one experiment population condition or another. The test assumptions that need to fulfilled before a dependent measure t-test can be done is a random sampling from a certain population, an interval or ratio scales of measurement, and a difference between mean scores while being normally distributed.

The main criterion for determine which two sample t-test to use starts with both groups being independent or dependent of one another. If the groups are dependent, the values must be normally distributed. The two groups must also be equal, or approximately equal, in variance in regards to the dependent variable.

The quantitative journal article I found is titled “Can Shoe Size Predict Penile Length?” by Shah and Christopher. The main hypothesis in the experiment was that there was a correlation between penile length and shoe size. The main results showed that the findings were not statistically significant for the relationship between penile length and shoe size. The linear regression resulted in an r2 of 0.012.