Ch. 15: Statistical Evolution of Data

• What are the two principle purpose that statistical methods serve?

  1. Statistics help organise and summarise research. So we can see what happened in the study and communicate the results to others.
  2. Statistics help the researcher answers the general questions that initiated the research by determining exactly conclusions are justified based on the results.
• Descriptive Statistics


  Statistical methods used to organise, summarise, and simplify the results obtained from research studies.
• Inferential Statistics


  Methods that use the results obtained from samples to help make generalisations about populations.
• Statistic


  A summary value that describes a sample.

  • They describe and/or summarise the entire set of scores in the sample.
  • They provide information about the corresponding summary values for the entire population.
• Parameters


  A summary value that describes a population. Each statistic has a corresponding parameter. As a result, the general purpose for inferential statistical techniques is to use sample statistics as the basis for drawing general conclusions about the corresponding population parameters.
• What is the main goal of descriptive statistics and the two general techniques that are employed to accomplish this goal?

  To organise and/or summarise a set of scores.

  1. Organise the entire set of scores into a table or graph that allows researchers to see the whole set of scores.
  2. Compute one or two summary values that describe the entire group.
• Frequency Distribution


  An organised display of a set of scores that shows how many scores are located in each category on the scale of measurement.

  1. The set of categories that make up the scale of the measurement.
  2. The number of individuals with scores in each of the cateogries.
• What is the advantage and disadvantage of a frequency distribution?

  • Advantage: Allows research to view the entire set of scores.
  • Disadvantage: Constructing a frequency distribution can be tedious.
• Histogram


  Shows a bar above each score so that the height of the bar indicates the frequency of occurence for that score. The bars for adjacent scores touch each other.
• Polygon


  Shows a point above each score so that the height of the point indicates the frequency. The straight line connect the points and additional straight lines are drawn down to the horizontal axis at each end to complete the figure.
• Bar Graph


  A frequency distribution graph in which vertical bar indicates the frequency of each score from a nominal or ordinal scale of measurement.
• Central Tendency


  A statistical measure that indentifies a single score that defines the centre of a distribution. The goal of central tendency is to identify the value that is most typical or most representative of the entire group.

  1. Mean
  2. Median
  3. Mode
• Mean


  A measure of central tendency obtained by adding the individual scores and dividing the sum by the number of scores.
• Median


  A measure of central tendency obtained by adding the individual scores and dividing the sum by the number of scores.
• Mode


  The score or category with the greatest frequency score in the distribution.
• Standard Deviation


  A measure of variability that describes the average distance from the mean; obtained by taking the square root of the variance.
• Variance


  Measures the variability of the scores by computing the average squared distance from the mean.

  First, measure the distance from the mean for each score and then square the distance and find the sum of squared distances.

  Secondly, for a sample, the average squared distance is computted by dividing the sum of squared by n - 1.
• Sample Variance


  Described as measuring the average squared distance from the mean, the actual calculations involve dividing the sum of squared distances by n - 1. Dividing n - 1 is necessary adjustment to ensure taht the sample variance provides an accurate representation of its population variance. This gives on average an accurate and unbiased picture of the populatio nvariance.
• Regression


  The process of finding the linear equation is called regression.
• Multiple Regression 


  A statistical tecnique used to studying multivariate relationships. The statistical process of finding the lienar equation that produces the msot accurate predicted values for Y using more than one predictor variable. This determines the specific values of b1 and b2, which produce the msot accurate predictions.
• Sampling Error


  The naturally occuring difference between a sample statistic and the corresponding population parameter.
• What does the sample error mean?

  A sample that does not provide and perfectly accurate picture of its population; there is some discrepancy or error between the information available from a sample and the true situation that exists in the general population.
• What is the fundamental problem for inferential statistics?

  To differentiate between research results that represent real patterns or relationships, and those that simply represent sampling error. The purpose of inferential statistics is to help researchers determine whether it really is just by chance or if there's an actual correlational relationship.
• Hypothesis Test


  A systematic procedure that determines whether the sample data provide convincing evidence to support the original research hypothesis. This can be viewed as a technique to ensure the internal validity. This is done to rule out chance as a plausible explanation for results.

  1. The patterns in the data represent systematic relationships among variables in the population.
  2. That the patterns in the data were produced by random variation from chance or sampling error.
• What are the five basic elements of a hypothesis test?

  1. The Null Hypothesis
  2. The Sample Statistic
  3. The Standard Error
  4. The Test Statistic
  5. The Alpha Level
• Null Hypothesis


  A statement about the populations or treatments being studied that says there is no chance, no effect, no difference, or relationship.
• The Sample Statistic


  The data from the research study are used to compute a sample statistic corresponding to the parameter specified in the null hypothesis. If the null hypothesis states that there is no difference between two popualtion means, the sample statistic would be the difference between two sample means. Or, if the null hypothesis states that the population correlation is zero, the sample statistic would be the sample correlation obtained in the research study.
• Standard Error


  A measure of the average, or standard, distance between a sample statistic and the corresponding population parameter.
• Test Statistic


  A summary value computed in a hypothesis test to measure the degree to which the sample data are in accord with the null hypothesis.
• Alpha Level


  The maximum probablity that the research result was obtained simply by chance; cut-offs are usually: .1, .25, and .5
• Statistically Significant Result


  A research study, a result that is extremely unlikely to have occured simply by chance.
• Type I Error


  Occurs when a researcher finds evidence for a significant result when, in fact, there is no effect in the population. The error occurs because the research has, by chance, selected an extreme sample that appears to show the existence of an effect when there is none.
• Type II Error


  Occurs when sample data do not show evidence of a significant effect, when, in fact, a real effect does exist in the population. This often occurs when the effect is so small that it does not show up in the sample.
• Effect Size


  The measured magnitude of a treatment effect or relationship.
• Cohen's d


  A standard measure of effect size computed by dividing the sample mean difference by the sample standard deviation.
• Percentage of Variance Accounted For

  This calculation involves measuring the percentage of variance for one variable that can be predicted by knowing a second variable.
• Confidence Intervals


  A range of values, centred around a sample statistics, used to estimate the magnitude of an unknown population value such as a mean difference or a correlation. The width of the interval is directly related to the degree of confidence in its accuracy.