# Descriptive vs. Inferential Statistics

Descriptive vs. Inferential Statistics AP PSYCHOLOGY

FRIDAY, SEPTEMBER 18

Descriptive Statistics 

Summarize data 

After collecting data, psychologists organize the data to create a frequency distribution – an orderly arrangement of scores indicating the frequency of each score or group of scores (shown visually has a frequency histogram or polygon)

Descriptive Statistics 

Measures of Central Tendency 

Describe the average or most typical scores for a set of research data or distribution

Mode, Median, Mean 

Mode can also be bimodal or multimodal or none at all

Descriptive Statistics 

Measures of Variability 

Describes the spread or dispersion of scores for a set of research data or distribution 

Range, variance, and standard deviation

Variance = squaring the difference between each value and the mean, summing the squared differences, and then taking the average of the sum

Standard Deviation = square root of the variance 

If the standard deviation approaches 0, scores are very similar to each other and very close to the mean

Normal Distribution 

Mean, median, and mode are all equal and located at the center.

“Bell curve”

68% of scores fall within one standard deviation

95% of scores fall within two standard deviations

99% of scores fall within three standard deviations

Very common in describing psychological characteristics 

It is used to determine portions of the population

Example 

1,000 subjects participate in a study on reaction time.

The reaction times of the participants are normally distributed with a mean of 1.3 seconds and a SD of 0.2 seconds. 

68% (680 out of 1000) would have a reaction time of 1.1-1.5

95% (950 out of 1000) would have a reaction time of 0.9-1.7

99% (990 out of 1000) would have a reaction time of 0.7-1.9

Percentiles 

Percentiles are another common descriptive statistic.

It is used frequently when reporting scores on standardized tests.

Percentiles express the standing of one score relative to all other scores in a set of data. 

If your SAT score is in the 85th percentile, then you scored higher than 85% of the other test takers.

Extreme Scores – Skewed Distributions 

Skewed = when most of the scores in a distribution land on one side of the scale or the other; not symmetrical; typically have a tail on one of the scale or the other

Inferential Statistics 

Experiments and descriptive statistics are typically used when measuring behavior in a sample of people drawn from a larger population. 

The sample size is typically denoted by N (the total number of subjects in the sample being studied) or n (the total number of subjects in a subgroup of the sample being studied)

Larger sample sizes are always better!

Researchers are more interested in what the data indicates for the population.

Inferential statistics indicate whether or not results based on the sample are significant enough to be applied to the larger population OR if the results were most likely caused by chance.

Researchers evaluate the differences in the dependent variable between the control and experimental groups.

Inferential Statistics 

If a difference in the dependent variable between the two groups is STATISTICALLY SIGNIFICANT, it means that the results were not likely to have happened by chance. 

Statistical significance indicates a high probability that the independent variable caused the change in the dependent variable.

Statistical significance does NOT refer to how important the results are.

Results are likely to be statistically significant when there is a large difference between the means of the two frequency distributions, when their standard deviations (SD) are small, and when the samples are large.

Researchers can use a variety of inferential statistics to determine statistical significance (chi square tests, t-tests, ANOVAs).

Inferential Statistics 

Each of these work to generate a probability value (p-value) that indicates how likely it is that the difference between the control and experimental groups is caused by chance and not the independent variable. 

The p-value must be ≤ .05 for statistical significance to exist

The lower the p-value, the more significant the results and the less likely they are caused by chance

A p-value of 0 will never happen because it is impossible to be 100% certain that the hypothesis is correct and that chance is not involved in any way.