Unit 2.0 and 2.1

• Descriptive Statistics:

  • Measures of Frequency
  • Measures of Central Tendency
  • Measures of Dispersion or Variation
  • Measures of Position
• Descriptive statistics are used to describe the basic features of the data in a study
• They provide simple summaries about the sample and the measures
• Together with simple graphics, they form the basis of virtually every quantitative analysis of data
• Descriptive statistics are used to summarize data in an organized manner by describing the relationship between variables in a sample or a population
• Calculating descriptive statistics is a vital first step when conducting research and should always occur before making inferential comparisons
• Gateway towards inferential statistics
• Further validates that your decision for inferential statistics is correct
• Strengthens your inferential statement in the conclusion
• Types of Variables:

  • Categorical Variables
  • Continuous Data
• Measures of Frequency:

  • Number of times a particular value occurs in the data
  • Relative frequencies can be expressed in ratio, rates, proportions, and percentages
• Measures of Central Tendency:

  • Mean: arithmetic average of values in a data set
  • Median: middle value in distribution when data are ranked
  • Mode: most common value in a data set
• Measures of Dispersion:

  • Range: difference between the lowest and highest value in a set
  • Variance and standard deviation: measures of spread revealing how close each observed value is to the mean
• Although measures of central tendency provide important information, they fail to capture the variability within the database
• Measures of dispersion/variation describe the degree to which values are similar or diverse
• Determining Standard Deviation using Excel
• Descriptive Statistics for Categorical Values:

  • Weighted Mean
  • Coding
• Normal Distribution:

  • A normal or Gaussian distribution is a symmetrical bell-shaped curve
  • The y-axis represents the relative probability of the observation
  • Normal distributions are always centered on the average value
  • The width of the curve is defined by the standard deviation
• To draw a normal distribution, you need to know the average measurement and the standard deviation
• In a normal distribution, data is distributed equally on both sides of the central value
• If the data is skewed, the distribution is not equal on both sides
• Descriptive Statistics

  • provide simple summaries about the sample and the measures
  • used to present quantitative descriptions in a manageable form
  • used to summarize data in an organized manner by describing the relationship between variables in a sample or a population
• Coverage of Descriptive Statistics

  1. Measures of Frequency (STDEV)
  2. Tells us how many times the value or investigated variable appears in the sample group
  3. Measures of Central Tendency (Variation)
  4. Tells us the position of the values on a normal distribution curve
  5. Measures of Dispersion or Variation
  6. Tells us how close or near a certain group of data are with one another
  7. Measures of Position
  8. Percentile, Decile, Quartile
• Categorical Variables

  • qualitative data or discrete data
  • Qualitative data in which the values are assigned to set of distinct groups or categories
  • can either be nominal, ordinal, or dichotomous
  • Example:
  • gender
  • civil status (qualitative data but not dichotomous instead they are multinomous)
• Continuous Data

  • quantitative or numerical
  • measurable amounts
  • can either be interval or ratio
• Measures of Frequency

  • number of times a particular value occurs in the data
• • Relative Frequencies - can be expressed in ration, rates, proportions, and percentages
• Measures of Central Tendency

  • are single values that attempt to describe a set of data by identifying their central position within that set of data
  • Mean - arithmetic average or the sum of values in a data set divided by the total number of observations
  • Median - middle value in distribution when the data are ranked in order from the lowest to highest
  • Mode - most common value in a data set.
• Mean

  
• Measures of Dispersion

  • describes the degree to which the values are similar or diverse
  • Range - difference between the lowest and the highest value in a set of values
  • Variance and Standard Deviation - measures of spread that reveal how close each observed value is to the mean of the entire data set
• Although the measures of central tendency provide important information in describing ones’ data, they fail to capture the variability within the database
• DESCRIPTIVE STATISTICS FOR CATEGORICAL VALUES

  • To be able to analyze categorical data we must need to convert qualitative data to numeric data by coding
• standard deviation

  • width of the curve
• To draw a normal distribution, you need to

  know:

  • The average measurement as this tells you where the center of the curve goes
  • The standard deviation of the measurements as this tell you how wide the curve should be and the width of the curve determines how tall it is
  • The wider the curve, the shorter
  • The narrower the curve, the taller
• If the tail is towards the right side of

  the value, it is positively skewed

  If the tail is towards the left side of the

  value, it is negatively skewed
• Hypothesis

  • an assumption or educated guess concerning one or more population parameters of a distribution.
  • could give a determination whether the observed difference is convincingly different from what was expected from the model
• Predictions about what the examination of appropriately collected data will show
• The statistical tool application determines the probability of an observed difference between means
• Determines if the observed difference is convincingly different from what was expected from the model
• In basic statistics, the application of the model is the null hypothesis