Statistical Analysis

• Once researchers have conducted their studies, they must summarize, organize, interpret, and analyze their data

• This comes before drawing any conclusions

• This is the premise behind statistics

Quantitative and Qualitative Data

• Researchers often start with quantitative data

  • This deals with raw numbers

• Qualitative data is descriptive

  • The data is investigative and often open-ended

Descriptive and Inferential Statistics

• Organizing and describing data is descriptive statistics

  • There are several steps and tools used such as frequency charts and graphs

• When making predictions about data, researches use inferential statistics

  • Researchers can predict or generalize how their data and the independent variable relates to a larger population

Qualitative Data: Descriptive Statistics

• Using a frequency distribution table, researchers can see how often a certain data point occurs

Types of Data and Scales of Measurement

• Discrete Data: Data that can be counted

  • Nominal Scale: Data without structure or order

  • Ordinal Scale: Count and order but not measurable

• Continuous Data: Data that can be measured

  • Interval Scale: Data with degrees of difference but no ratio between them

  • Ratio Scale: Data that processes a meaningful measurement with a zero value

• Dichotomy Scale: Having two categories when organizing data

• Trichotomy Scale: Having three or more categories

Central Tendency: Mode, Mean, and Median

• When using central tendency, researchers are identifying an estimated “center” of the data distribution

• Mean is the average of the data set

• Mode is the most frequent data point

• Median is found at the exact middle of the data set

  • This is found by counting inwards from the top and bottom

  • If there are two ‘middle numbers,’ the two are averaged

Variation: Range and Standard Deviation

• Central tendency provides a snapshot of the data but does not reveal how the data is dispersed

• Range and standard deviation allow researchers to understand the variation between data points

• Range is the difference between the highest and lowest value point

  • This only identifies the distance between the extremes

  • It does not reveal distance from the mean, nor any other value point

• Standard deviation allows researchers to indicate the average difference from the mean for a set of scores

  • The higher the standard deviation, the less similar the scores

Frequency Distribution: Normal, Positive, and Negative Skews

• A symmetrical distribution is produced when a large group of people’s variables are tested such as intelligence, shoe size, height, etc.

  • This symmetrical distribution is called a normal distribution or bell curve

  • In order to achieve the perfect bell curve, the mode, median, and mean are at the 0-point value

• Most data will not have a perfect distribution curve

  • A positive skew occurs when scores pull the mean toward the higher end of the scores

  • A negative skew occurs when scores pull the mean toward the lower end of the scores

Correlation and Causation

• Correlational studies do not imply causation

• Correlational studies do, however, offer researchers the opportunity to determine the relationship between two variables

Correlational Studies

• Scatter plots are used by researchers to understand the relationship between two variables

• This strength of those two variables is called the correlation coefficient

  • The closer the value is to +1.0 or -1.0, the stronger the relationship

• A positive relationship between two variables can be 0 through +1.0

  • This means the variables increase or decrease together

• A negative relationship can range from 0 to -1.0

  • This means one of the variables increases as the other decreases

• No correlation means there is not a relationship between the variables

Inferential Statistics: Statistical Significance

• When drawing conclusions about data, researchers use inferential statistics

• The likelihood that data collection was a result of intentional manipulation and not chance is called statistical significance

  • Researchers are looking to establish a p-value

  • The closer it is to 0, the more they can be sure that data supports their hypothesis and outside factors have not influenced their results