Interpreting Results - AP Psychology

Statistics play a big role in much of the research in the field of psychology. In studying groups of people and individuals, their behaviors, reactions, etc. a researcher will have lots of numerical data on their hands. Statistics is the analysis of this numerical data.

A Pearson correlation between two variables indicates that as one variable increases, another variable either increases or decreases by some amount in a linear manner.

Correlations range between and , with signifying the strongest possible negative correlation between two variables, signifying the strongest possible positive correlation, and signifying the complete absence of any correlation between two variables.

Correlation coefficients range from -1 to 1, with the strongest correlations being closer to -1 or 1. A correlation of 0 indicates no relationship between two variables. Negative correlations can be as strong or stronger than positive correlations; the most important factor is the magnitude of the correlation.

An illusory correlation occurs when someone thinks that two variables are related, but they are actually not (they have a correlation of 0).

The median is the middle number in a data set. For example, the median of {3, 7, 4, 5, 8} is 5. The terms must first be placed in increasing order: {3, 4, 5, 7, 8}. From here, it becomes evident that 5 is the middle term, or median.

A study's validity is its ability to scientifically measure the concepts it was designed to measure. A study's reliabilityis its ability to yield similar results when replicated in a similar setting.

Because Carol's study could be replicated but does not answer the question it was designed to answer her study is reliable, but not valid.

The number describing two variables relationship is the correlation coefficient. This could show a positive correlation (+ number) or a negative correlation (- number). The further from 0 the coefficent is the stronger the correlation.

The mean is the average of a data set. On the other hand, the median is considered to be the 50th percentile—that is cutting the entire data set in half and representing the exact middle of the data set. The mean may be skewed depending on the data set. For instance, the median may be 50 but because of a few higher numbers, the mean could be 56. Using the mean as a measure of central tendency may cause the distribution to be a bit lopsided. Percent error is a statistical measure of the marginal error of actual results compared to expected results; therefore, percent error would not be the correct answer. Additionally, standard deviation is the measurement of the deviation from a group as a whole. This calculation is often conducted using averages (means); thus, the options standard deviation and standard deviation of the mode would also be incorrect.

Type II error—also called a false negative—occurs when a researcher incorrectly fails to reject a false null hypothesis. In other words, the researcher should have rejected the null hypothesis in favor of the experimental hypothesis. In this case, the researcher should have found evidence in favor of the experimental hypothesis that ginseng consumption has a significant effect on memory; however, the researcher failed to do so because of some experimental error (i.e. random or systematic, the problem does not specify).

2.3 percent of individuals fall two standard deviations above the mean in a normal distribution. 2.3% of 1000 individuals is 23 individuals that fall above this cutoff.

Convert the percentage into a ratio.

Create a ratio using the total number of the sample size. Use the variable as a representation of the number of individuals that fall two standard deviations above the mean.

Create a proportion using the two ratios.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

Any correlation between .30 and .69 is considered moderate in strength. Anything above .60 is considered strong. Anything below .30 is considered weak or no correlation.

A type I error occurs when a null hypothesis is rejected when researchers should have failed to reject the null hypothesis, in other words, when the researchers reject a true hypothesis. Remember, a null hypothesis is the assumption that there is no difference between the groups participating in the study. So if a type I error occurs, that means that the researchers are stating there is a difference between the groups when there really is not a difference. A Type II error involves the acceptance of a false hypothesis.

A type II error occurs when researchers fail to reject their null hypothesis when they should have rejected it. A null hypothesis is the assumption that there is no difference between the groups being studied. So if a type II error occurs, that means that the researchers are stating there is not a difference between the groups when there really is one.

Central tendency measures include the mean, median, and mode. In this case, the median would be best because several outliers skew this data set (e.g. perfect scores). The mean would be influenced strongly by these outliers.

A correlation coefficient is a measure of the relationship between two variables. Correlation coefficients range from -1 to +1. For this reason -1.5 is incorrect because it is not possible to have a correlation coefficient less than -1. This question is asking for a coefficient with a strong inverse relationship. A positive number indicates a direct relationship, while a negative number indicates an indirect or inverse relationship. The specific number indicates the strength of the relationship. If the correlation coefficient is closer to -1 or +1, then it is said to be strong. As the number moves closer to zero, the strength of the relationship decreases; therefore, -0.90 is the best answer.

In order to calculate the mean (also called arithmetic average) we need to add all the values together and divide by the number of values. In this case, the total sum is 87 and the number of values is 12, so we perform the following calculation to obtain our mean:

To find the median, we simply arrange the values in order from least to greatest and identify the middlemost number. However, since 12 is an even number, there will not be one single middle value– therefore, we find the average of the two middlemost values. Arranged in ascending order, the data set is:

The 6th and 7th values are 6 and 7, so we know our median is the average of 6 and 7.

The mode is the value that occurs most frequently in the data set. Here, 6 occurs three times and no other number occurs more than twice, which means 6 is our mode.

The "dependent variable" is indicative of the outcome of an experiment, and is recorded as evidence to attempt to provide support for or against a thesis. The independent variable is indeed measured; however,its quantities are irrelevant to an experiment. Control and random variables are not recorded and are only useful when considering the changes to dependent variable.

Statistical significance is a statistical criterion for rejecting the assumption of no difference between groups in a particular study. In order to establish statistical significance, researchers typically look for a p value of less than .05, which indicates that the study's findings were not obtained due to chance or error.