Hi,

I did some hypothesis testing exercises and I cross checked the result with Maple. I just used following vectors for an unpaired test

a := [88, 89, 92, 90, 90];

b := [92, 90, 91, 89, 91];

I ended up with the following solution:

HFloat(1.5225682336585966)

HFloat(-3.122568233658591)

for a 0.95 confidence interval.

Using

TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed)

and

TwoSampleTTest(a, b, 0, confidence = .975, summarize = embed)

I get following results:

-2.75177 .. 1.15177

-3.13633 .. 1.53633

respectively. I can not explain the discrepancy.

Best regards,

Oliver

PS:

Maple Code in case files won´t be attached.

Unpaired t Test

restart;

Unpaired test-test dataset

a := [88, 89, 92, 90, 90];

b := [92, 90, 91, 89, 91];

The seÂ² estimate is given by:

seÂ²=var(a)+var(b)+2*cov(a*b)=var(a)+var(b)

seÂ²=

sigma[a]^2/Na+sigma[b]^2/Nb;

with Na, Nb being the length of vector a and b respectively.

2 2

sigma[[88, 89, 92, 90, 90]] sigma[[92, 90, 91, 89, 91]]

---------------------------- + ----------------------------

Na Nb

sigma[a]^2;

and

sigma[b]^2;

are approximated by

S[a]^2;

and

S[b]^2;

2

sigma[[88, 89, 92, 90, 90]]

2

sigma[[92, 90, 91, 89, 91]]

2

S[[88, 89, 92, 90, 90]]

2

S[[92, 90, 91, 89, 91]]

with

S[X]^2;

defined as

S[X]*`Â²` = (sum(X[i]-(sum(X[j], j = 1 .. N))/N, i = 1 .. N))^2/N;

2

S[X]

2

/ / N \\

| | ----- ||

| N | \ ||

|----- | ) ||

| \ | / X[j]||

| ) | ----- ||

| / | j = 1 ||

|----- |X[i] - ----------||

\i = 1 \ N //

S[X] ï¿ï¾² = ----------------------------

N

with(Statistics);

Sa := Variance(a);

HFloat(2.1999999999999993)

Sb := Variance(b);

HFloat(1.3000000000000003)

Now we are ready to do hypothesis testing (0.95).

We have (with k=min(Na,Nb)=5):

C = mean(a)-mean(b); Deviation := t_(alpha/a, k-1)*se(Sa/k-Sb/k);

c := Mean(a)-Mean(b); deviation := 2.776*sqrt((1/5)*Variance(a)+(1/5)*Variance(b));

HFloat(-0.7999999999999972)

HFloat(2.3225682336585938)

upperlimit := c+deviation; lowerlimit := c-deviation;

HFloat(1.5225682336585966)

HFloat(-3.122568233658591)

Execution of built in student test

TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed);