Summary advanced statistics
Blocks: groups of similar experimental unites, entered in the model to reduce the error variance
Confidence interval (C.I): the width of the interval indicates how precisely we have estimated the
unknown parameter. Estimate ± (table 2 value T) x (standard error of the estimator).
Controle treatment: 1) to monitor experimental conditions or 2) standard method for comparison or
3) placebo
Covariate: quantitative variable X measured along with Y
Estimate: the outcome of the estimator from the experiment or sample
Experimental units: The physical entity to which the treatment is randomly assigned or the subject
that is randomly selected from one of the treatment populations
Experimental units: units to which the treatments are randomly allocated
Factor level: the level of the factor In the experiment
Factor: controlled variable (qualitative or quantitative)
Four defining elements of T-procedures: 1) The parameter of interest 2) the estimator 3) the
standard error of the estimator 4) the degrees of freedom of the relevant T-distribution
Hypothetical population: experimental research population
Inference: drawing conclusions about a population from a limited set of observations.
Measurement units: units on which we do the measurements
Physical population: observational research population
P-value: probability under H0 for the outcome of the test statistics T and anything more extreme,
supporting Ha
Replications: Repetitions of treatments receiving the same treatments
Response variable: the variable interest y
Standard deviation: σ
Standard error: indication of how uncertain the estimate is
Test exactly: calculate P value (do not use RR)
Treatments: combinations of the factor levels used in the experiment
Unbiased estimator: estimator would on average would give the correct value, if one would repeat
the experiment ‘one million’ times.
Eight steps of a test-procedure:
1) The null hypothesis H0 and the alternative hypothesis Ha
2) The definition of the test statistics (the formula of what to calculate)
3) The behaviour of the test statistic under H0 (null distribution)
4) The qualitative behaviour of the test statistic under Ha
5) Choose the type of P-value (left/right/two-tailed)/ type of RR
Data is used in the following steps
6) The outcome of the test statistics
7) The appropriate P-value, and compare it to α. Or if the outcome is in the RR or not
8) State that H0 is rejected or not, that Ha is proven or not, and your conclusion in words in erms
relevant to the particular problem
,Lecture 1: Confidence intervals and hypothesis testing
3 types of T tests:
1) We assume that data are independent observations from a normal distribution one
sample T test.
2) Two response variables x and y, and interest is in µxy. It is assumed that the differences (d)
between x and y are normally distributed. So the model is, the di ‘s are independent drawing
from N(µd, σd) two sample T test
3) Interest is in the difference between two population means, µ1 and µ2. It is assumed that the
observations come independently from two normal distributions. It is also often assumed
that the two distributions have the same variance.
Assumptions are:
- Normality QQ plot of the observations/D’s/deviations from the mean
- Equal variance sample standard deviations need to be equal or side-by-side box plot
but mostly levene’s test for equality is used.
- Independence correct randomisation,
Null distribution: t follows a t-distributin with Df (x)
Situation Parameter Estimator SE Df
1 µ ӯ s/ √(N) N-1
2 µd d̄ Sd/ √(N) N-1
3A µ1 - µ2 Ӯ1 – ӯ 2 Sp* N1+N2 -2
1 1
3B µ1 - µ2 Ӯ1 – ӯ 2
√ +
N1 N2
S1 S2 ?
(σ1=σ2) √ +
N1 N2
Parameter estimator − parameter value under H 0
t=
¿¿
Confidence interval (CI) : values that we want to consider with some confidence, interval is a range
of likely values for a parameter. Often the confidence level is 0,95.
Estimate ± constant * standard error constant in table 2
, Note that SPSS will always give a 2-sided test significant when one sided is preferred, divide with
2.
Blocks: groups of similar experimental unites, entered in the model to reduce the error variance
Confidence interval (C.I): the width of the interval indicates how precisely we have estimated the
unknown parameter. Estimate ± (table 2 value T) x (standard error of the estimator).
Controle treatment: 1) to monitor experimental conditions or 2) standard method for comparison or
3) placebo
Covariate: quantitative variable X measured along with Y
Estimate: the outcome of the estimator from the experiment or sample
Experimental units: The physical entity to which the treatment is randomly assigned or the subject
that is randomly selected from one of the treatment populations
Experimental units: units to which the treatments are randomly allocated
Factor level: the level of the factor In the experiment
Factor: controlled variable (qualitative or quantitative)
Four defining elements of T-procedures: 1) The parameter of interest 2) the estimator 3) the
standard error of the estimator 4) the degrees of freedom of the relevant T-distribution
Hypothetical population: experimental research population
Inference: drawing conclusions about a population from a limited set of observations.
Measurement units: units on which we do the measurements
Physical population: observational research population
P-value: probability under H0 for the outcome of the test statistics T and anything more extreme,
supporting Ha
Replications: Repetitions of treatments receiving the same treatments
Response variable: the variable interest y
Standard deviation: σ
Standard error: indication of how uncertain the estimate is
Test exactly: calculate P value (do not use RR)
Treatments: combinations of the factor levels used in the experiment
Unbiased estimator: estimator would on average would give the correct value, if one would repeat
the experiment ‘one million’ times.
Eight steps of a test-procedure:
1) The null hypothesis H0 and the alternative hypothesis Ha
2) The definition of the test statistics (the formula of what to calculate)
3) The behaviour of the test statistic under H0 (null distribution)
4) The qualitative behaviour of the test statistic under Ha
5) Choose the type of P-value (left/right/two-tailed)/ type of RR
Data is used in the following steps
6) The outcome of the test statistics
7) The appropriate P-value, and compare it to α. Or if the outcome is in the RR or not
8) State that H0 is rejected or not, that Ha is proven or not, and your conclusion in words in erms
relevant to the particular problem
,Lecture 1: Confidence intervals and hypothesis testing
3 types of T tests:
1) We assume that data are independent observations from a normal distribution one
sample T test.
2) Two response variables x and y, and interest is in µxy. It is assumed that the differences (d)
between x and y are normally distributed. So the model is, the di ‘s are independent drawing
from N(µd, σd) two sample T test
3) Interest is in the difference between two population means, µ1 and µ2. It is assumed that the
observations come independently from two normal distributions. It is also often assumed
that the two distributions have the same variance.
Assumptions are:
- Normality QQ plot of the observations/D’s/deviations from the mean
- Equal variance sample standard deviations need to be equal or side-by-side box plot
but mostly levene’s test for equality is used.
- Independence correct randomisation,
Null distribution: t follows a t-distributin with Df (x)
Situation Parameter Estimator SE Df
1 µ ӯ s/ √(N) N-1
2 µd d̄ Sd/ √(N) N-1
3A µ1 - µ2 Ӯ1 – ӯ 2 Sp* N1+N2 -2
1 1
3B µ1 - µ2 Ӯ1 – ӯ 2
√ +
N1 N2
S1 S2 ?
(σ1=σ2) √ +
N1 N2
Parameter estimator − parameter value under H 0
t=
¿¿
Confidence interval (CI) : values that we want to consider with some confidence, interval is a range
of likely values for a parameter. Often the confidence level is 0,95.
Estimate ± constant * standard error constant in table 2
, Note that SPSS will always give a 2-sided test significant when one sided is preferred, divide with
2.
