Chapter 5:  Hypothesis Tests with Means of Samples

The Distribution of Means

n    Comparison distributions considered so far were distributions of individual scores

n    Mean of a group of scores

n   Comparison distribution is distribution of means

The Distribution of Means

n    Distribution of means

n   Distribution of the means of each of a very large number of samples of the same size (with each sample randomly taken from the same population of individuals)

The Distribution of Means

n    Characteristics

n   Its mean is the same as the mean of the population of individuals

n   Its variance is the variance of the population divided by the number of individuals in each of the samples

The Distribution of Means

n    Characteristics

n   Its standard deviation is the square root of its variance

n   Shape: it is approximately normal if either:

n  Each sample is of 30 or more individuals or

n  The distribution of the population of individuals is normal

Review of the Different Kinds of Distributions

n    Distribution of a population of individuals

n    Distribution of a particular sample

n    Distribution of means

 

 

Comparison of Three Types of Distributions

 

Hypothesis Testing With a Distribution of Means

n    It is the comparison distribution when a sample has more than one individual

n    Find a Z score of your sample’s mean on a distribution of means

 

Estimation, Standard Errors, and Confidence Intervals

n    Estimating the mean: point estimates

n    Accuracy of a point estimate

n    Interval estimates

n   Confidence limits

n   95% confidence interval

n   99% confidence interval

Estimation, Standard Errors, and Confidence Intervals

n    Steps for figuring confidence limits

   1. Figure the standard error

 

 

 

   2. Figure the raw scores for 1.96 standard errors (95% confidence interval) or 2.57 standard errors (99% confidence interval)    above and below the sample mean

 

Estimation, Standard Errors, and Confidence Intervals

n    Subtle logic of hypothesis testing

n    Confidence intervals and hypothesis testing

Controversies and Limitations

n    Confidence intervals or significance tests?

n   Confidence intervals

n  Give additional information

n  Focus attention on estimation

n  Less likely to be misused by researchers

n   Significance tests

n  Necessary for some advanced statistical procedures

Reporting in Research Articles

n    Z test

n    Standard error, SE, SEM

n   Standard error bars