Statistical Analysis

Question 1

report on the data from a total population that is measured, recorded or found to occur

Answer 1

Descriptive statistics

Question 2

Descriptive statistics include four major types of data analysis

Answer 2

• Measures of Frequency (i.e. how often a datum occurs)
  o Count, Percent, Frequency
• Measures of Position (i.e. the relative location of a particular datum in a data set)
  o Percentile Ranks, Quartile Ranks
• Measures of Central Tendency (i.e. the center of the data)
  o MEAN - simple arithmetic average of the numbers, calculated by adding up all the data numbers in the data set and then dividing the total number of data in the data set.
  o MEDIAN – the middle number of a data set; when the set has an even number of data points, then the median is the average of the two middle-most numbers
  o MODE – the most frequent number in the data set; if there are two most frequent numbers in the set, the data set is bi-modal; if more than two, it is multimodal
• Measures of Dispersion or Variation (i.e. the spread of the data about a central value)
  o RANGE – the difference between the highest number and lowest number in a data set
  o VARIANCE - a measure of how spread out a data set is; it is computed as the average squared deviation of each number from the data set’s mean.
  Variance (σ²) = sum (each number – mean)² / total numbers in the set
  o STANDARD DEVIATION - a measure of how close the numbers in the data set are to the mean; it is computed as the square root of the variance
  Standard deviation (σ) = √𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣

Question 3

NORMAL CURVE/STANDARD DEVIATIONS

SOURCE: 2005 APA Conference, Dale Case

• About 68% of the data will lie within one standard deviation (σ) of the mean (plus or minus)
• 95% of the data will lie within two standard deviations (2σ) of the mean (plus or minus)
• 99% of the data will lie within three standard deviations (3σ) of the mean (plus or minus)

Answer 3

Question 4

used to make predictions or inferences from a data sample of the entire population (e.g. survey). Inferential statistics are used when the examination of the entire population is not possible or convenient, and you desire to make generalizations or conclusions about a population from the data sample you’ve obtained.

Answer 4

Inferential statistics

Question 5

Inferential statistics include the following common types of data analysis:

Answer 5

• Linear Regression
  o Used to understand the linear relationship between a dependent variable (y) and an independent variable (x) in a data set (i.e. how the change in one variable can be used to estimate the change in another variable, and provides a “best fit” line to that relationship, based on the simple formula y=a+bx).
• Correlation Analysis (Pearson’s r, Spearson, Chi Square)
  o Used to understand the degree to which two variables are dependent on each other (i.e. measure of the strength of the linear relationship between two variables). The correlation can be negative (one variable decreases while the value of the other increases) or positive (both variables decrease or increase together).
• Statistical Significance (t-test)
  o Used to compare two separate, non-overlapping groups or data sets. It compares the means of the two groups (e.g. test scores for boys, girls). With more groups, use ANOVA.
• Analysis of Variance (ANOVA)
  o Used to compare two or more separate, non-overlapping groups or data sets. It compares the means of the groups (e.g. a particular political position for Democrats, Independents, Republicans, Libertarians).