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Day 1: Measurement

Before you conduct a study, use your theory to answer five questions: (1) what are you trying to prove, (2) what is it like in practice, (3) who is predicting whom, (4) who is being studied, and (5) what do the numbers mean? Theories are used to guide research; models are used to test theories. Because theories are composed of constructs, they are untested theoretical realities. But models are built for the purpose of being tested; they are composed of variables.

NOW YOU CHOOSE:
    Day 1: Measurement
    A Bit More About Measurement
    Even More About Measurement 1
    Even More About Measurement 2
    Even More About Measurement 3
    Basic Facts About Measurement
    Audio Lectures
    Videos
    Vocabulary
    Quiz 1
    Summary

Day 2: Central Tendency

The goal is to find a way to summarize a large group of numbers. One part of that process is to find a group’s representative. We want one number that will tell us about the entire group. There are 3 basic choices: mean, median and mode. The mean is hypothetical average person. The median is the middle-most person. The mode is the most popular person.

NOW YOU CHOOSE:
   Day 2: Central Tendency
   A Bit More About Central Tendency
   Even More About Central Tendency
   More Examples
      More Mean Examples
      More Median Examples
      Median Is Middle Of Distribution
      More Mode Examples
   Impact of Outlying Scores
      On The Mean
      On The Median
      On The Mode
   How To Calculate Central Tendency
      Calculating The Mean
      Calculating The Median
      When There’s No Middle-Most Score
      Calculating The Mode
   Formulas For Central Tendency
   Basic Facts About Central Tendency
   Audi: Lectures
   Videos
   Vocabulary
   Quiz 2
   Summary

 

 

 

 

 

 

 

 

 

Day 3: Dispersion

We found the middle of the group because most people score about the same on any variable we measure. Now that you’ve found a representative for the group, how representative is the mean? Is the group unified and nearly everyone has the same score? Or are there wide fluctuations within the group? We want one number that will tell us if the scores are very similar to each other or if the group is composed of heterogeneous scores.

ll measures of dispersion get larger when the distribution of scores is more widely varied. A narrow distribution (a lot of similar scores) has a small amount of dispersion. A wide distribution (lots of different scores) has a wide distribution. The more dispersion, the more heterogeneous (dissimilar) the scores will be.

There are five measures of dispersion:

Range

Mean Absolute Deviation (Mean Variance)

Sum of Squares

Variance

Standard Deviation

NOW YOU CHOOSE:
    Day 3: Dispersion
    A Bit More About Dispersion
    Even More About Dispersion
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    How To Calculate
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    Formulas For Dispersion
    Practice Problems
    More Practice Problems
    Basic Facts About Dispersion
    Audio: Lectures
    Vocabulary
    Quiz 3
    Summary

 

 

 

Day 4: z-Score

An entire distribution can often be reduced to a mean and standard deviation. A z-score uses that information to indicate the location of an individual score. Essentially, z-scores indicate how many standard deviations you are away from the mean. If z = 0, you’re at the mean. If z is positive, you’re above the mean; if negative, you’re below the mean. In practical terms, z scores can range from -3 to +3.

 

 

Day 5: Correlation

This is the first 2-variable model we’ll consider. Both variables (designated X and Y) are measures obtained from the same subjects. Basically, a mathematical representation of a scatterplot, a correlation indicates whether the variables move together in the same direction (+ correlation), move in opposite directions (- correlation) or move separately (0 correlation). Correlations are widely used to measure reliability, validity and commonality.

 

NOW YOU CHOOSE:
    Day 5: Correlation
    Bit More About Correlation
    Even More About Correlation
    Calculate Correlation
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1            Sim2             Sim3
        Sim4            Sim5             Sim6
        Sim7            Sim8             Sim9
    Basic Facts About Correlation
     Audio: Lectures
    Vocabulary
    Formulas
    Quiz 5
    Summary

 

Day 6: Regression

With regression, you can make predictions.
When there is a strong correlation between two variables (positive or negative), you can make accurate predictions from one to the other. If sales and time are highly correlated, you can predict what sales will be in the future…or in the past. You can enhance the sharpness of an image by predicting what greater detail would look like (filling in the spaces between the dots with predicted values). Of course the accuracy of your predictions, depends on the strength of the correlation. Weak correlations produce lousy predictions.

 

Day 7: Probability

 Moving from describing events to predicting their likelihood involves probabilities, odds, and the use of Fisher’s F test. Probabilities compare of an event to the total number of possible events (4 aces out of 52 cards equals a probability of .077). Odds compare sides: 4 aces in a deck against 48 cards that aren’t aces (which equals odds of 1:12).

Analysis of Regression (ANOR) is an application of probability to linear regression. The ANOR uses a F-test, which is a ratio of variances. It is the ratio of understood variance to unexplained variance. To find the likelihood that a regression can be explained by a straight line, the number derived from an F test is compared to a table of probabilities. If the value you calculated is bigger than (or equal to) the value in the book, the pattern you see in the data is unlikely to be due to chance.

  

NOW YOU CHOOSE:
    Day 7: Probability
    Bit More About Probability
    Even More About Probability
    Even More About ANOR
    Calculate ANOR
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1       Sim2        Sim3
    Basic Facts About Probability
     Audio: Lectures
    Vocabulary
    Formulas
    Quiz 7
    Summary

Day 8: Independent t-Test

A t-test asks whether two means are significantly different. If the means, as representatives of two samples of the same variable, are equal or close to equal, the assumption is that the differences seen are due to chance. If the means are significantly different, the assumption is that the differences are due to the impact of an independent variable.

 

NOW YOU CHOOSE:
    Day 8: Student’s t-Test
    Bit More About t-Test
    Even More About t-Test
    How to Calculate t-Test
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1           Sim2            Sim3
        Sim4           Sim5            Sim6
        Sim7           Sim8            Sim9
    Basic Facts About t-Test
     Audio: Lectures
    Vocabulary
    Formulas
    Quiz 8
    Summary

Day 9: One-way ANOVA

 When more than 2 groups are to be compared, multiple t-tests are conducted because of the increased likelihood of Type I error. Instead, before subgroup comparisons are made, the variance of the entire design is analyzed. This pre-analysis is called an Analysis of Variance (ANOVA for short). Using the F-test (like an Analysis of Regression), an ANOVA makes a ratio of variance between the subgroups (due to the manipulation of the experimenter) to variance within the subgroups (due to chance).

 

NOW YOU CHOOSE
    Day9: 1-Way ANOVA
    Bit More About 1-Way ANOVA
    Even More About 1-Way ANOVA
    Calculate 1-Way ANOVA
    Practice Problems
    More Practice Problems
    Word Problems
        Sim1        Sim2         Sim3
        Sim4        Sim5         Sim6
        Sim7        Sim8         Sim9
     Audio: Lectures
    Vocabulary
    Formulas
    Quiz 9
    Summary

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