Stats Q4L1

• Bivariate data


  Data that involve two variables that are taken from a sample or population
• Univariate data are data that involve only a single variable.
• Correlation Analysis – is a statistical method used to determine whether a relationship between two variables exists.
• A scatterplot shows how the points of bivariate data are scattered.
• The line that is closed to the points is called the trend line. It indicates the direction – whether positive or negative as denoted by the slope of the line.
• In a positive correlation, high values in one variable

  correspond to high values in the other variable.
• In a negative correlation, high values in one variable

  correspond to low values in the other variable.
• The closer the points are to the line, the stronger is the correlation.
• A perfect correlation exists when all the points fall in the trend line.
• A perfect correlation maybe positive or negative.
• The most common coefficient of correlation is known as the Pearson product-moment correlation coefficient, or Pearson’s r.
• It is a measure of the linear correlation (dependence) between two variables X and Y, giving a value between +1 and −1.
• Pearson product-moment correlation coefficient was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s.
• If the trend line contains all the points in the scatterplot and the line points to the right, we conclude that there is a perfect positive correlation between the two variables. The computed r is 1.
• If all the points fall on the trend line that point to the left, then there exists a perfect negative correlation between the pair of variables. The computed value of r is -1.
• If the trend line does not exist, there is no correlation between the pair of variables. This is confirmed by the computed value of r which is 0.
• ±1 = Perfect positive/negative correlation
• ±0.71 to ±0.99 = Strong positive/negative correlation
• ±0.51 to ±0.70 = Moderately positive/negative correlation
• ±0.31 to ±0.50 = Weak positive/negative correlation
• ±0.01 to ±0.30 = Negligible positive/negative correlation
• 0 = No correlation
• The t-test is a statistical test procedure that tests whether there is a significant difference between the means of two groups.
• There are three different types of t-tests. The one sample t-test, the independent-sample t-test and the paired-sample t-test
• We use the one sample t-test when we want to compare the mean of a sample with a known reference mean.
• We use the t-test for independent samples when we want to compare the means of two independent groups or samples. We want to know if there is a significant difference between these means.
• The t-test for dependent samples (paired t-test) is used to compare the means of two dependent groups.
• To calculate the t-value, we need two values. First, we need the difference of the means and second, the standard deviation from the mean. This value is called the standard error.
• One Sample t-Test – Used to test whether the mean of single variable differs from a specified constant.
• The independent samples t-test is used to test comparative research questions. That is, it tests for differences in two group means or compares means for two groups of cases.
• Paired Samples t-Test is used to compare the means of two variables for a single group.