Statistical Analysis for Education and Psychology Researchers

Confidence Intervals for Paired Difference t-test

The following section of SAS code computes the 95 per cent CI for difference in means
when samples are paired (related) as follows:

data a; set a;

diff= occ2 − occ1;

proc summary data=a ;

var diff;

output out=out mean=mean stderr=stderr n=n;

run;

data b; set out;

alpha=.05;

df=n−1;

tobs=mean/stderr;

t=round (tinv (1−alpha/2,df), .001);

lc=round(mean−t*stderr, .001);

uc=round(mean+t*stderr, .001);

proc print data=b split='*' noobs;

var n alpha tobs lc uc;

title1 'Confidence intervals for difference between

paired means';

label alpha='Alpha’

n ='Sample size'

tobs='t-ratio'

df ='Degrees of Freedom'

sediff='Standard error'

lc ='Lower Confidence Limit'

uc ='Upper Confidence Limit';

Output from this SAS code is shown:
Confidence intervals for difference between paired means
Sample size Alpha t-ratio Lower Confidence Limit Upper Confidence Limit
10 0.05 0.96101 −5.009 l2.409

The interpretation is exactly the same as in the worked example.

8.6 Introduction to Analysis of Variance (ANOVA)

Analysis of variance is a statistical hypothesis testing procedure first developed by Fisher
(1953) to analyse data generated by experimental designs. The ANOVA approach
enables an investigator to assess the causal influence of two or more independent
variables (treatments), and possible interactions of these treatment effects on a single
response (outcome) variable. In a classical experimental design to compare different
treatments, each treatment is applied to several experimental units, and the assignment of
units to treatments is random. In many designs the number of units per treatment are
equal and this is then called a balanced design. In psychology and education the

Statistical analysis for education and psychology researchers 308