CHAPTER 13: UNDERSTANDING RESEARCH RESULTS- STATISTICAL
SAMPLES AND POPULATIONS
•Inferential statistics are necessary because the results of a given study are
based on data obtained from a single sample of research participants.
•If researchers ever study entire populations; their findings are based on
•In addition to describing sample data, we want to make statements about
oWould the results hold up if the experiment were conducted repeatedly,
each time with a new sample?
Definition of Inferential Statistic: statistics designed to determine whether
results based on sample data are generalizable to a population
•Used to determine whether we can, in fact, make statements that the results
reflect what would happen if we were to conduct the experiment again and
again with multiple samples.
oWhether we can infer that the difference in the sample means reflects
a true difference in the population means.
Example: People in one state might tell you that 57% prefer the Democratic
candidate and that 43% may favor the Republican candidate for office.
•Reports say that these results are accurate to within 3 percentage points,
with a 95% confidence level.
•The researchers are very confident that if they were able to study the entire
population rather than a sample, the actual percentage who preferred the
Democratic candidate would between 60% and 54%
•The percentage preferring the Republican would be 46% and 40%
•Researcher could predict with a great deal of certainty that the Democratic
candidate will win because there is no overlap in the projected population
•Equivalence of groups is achieved by experimentally controlling all other
variables or by randomization.
•The assumption is that if the groups are equivalent, any differences in the
dependent variable must be due to the effect of the independent variable.
•It is also true that the difference between any two groups will almost never be
oThere will be some difference in the sample means, even when all of
the principles of experimental designs are utilized; this happens
because we are dealing with samples rather than populations.
•Random or chance error will be responsible for some difference in the means
even if the independent variable had no effect on the dependent variable.
•THE POINT IS THAT THE DIFFERENCE IN THE SAMPLE MEANS
REFLECTS ANY TRUE DIFFERENCEIN THE POPULATION MEANS,
PLUS ANY RANDOM ERROR.
•Inferential statistics give the probability that the difference between means
reflects random error than a real difference.
NULL AND RESEARCH HYPOTHESIS
•Statistical inference begins with a statement of the null hypothesis and a
research (or alternative) hypothesis.
Null Hypothesis: The hypothesis used for statistical purposes that the variables
under investigation are not related in the population, that any observed effect
based on sample results is due to random error.
(null hypothesis) : the population mean of the no-model group is equal to
the population mean of the model group
•Independent variable had no effect
• Used because it is very precise
oThe population means are exactly equal
oPermits us to know precisely the probability of the outcome of the
study occurring if the null hypothesis is correct.
oThe null hypothesis is rejected when there is a low probability that the
obtained results could be due to random error.
This is what is meant by statistical significance.
Statistical significance: Rejection of the null hypothesis when
an outcome has a low probability of occurrence (usually .05 or
less) if, in fact, the null hypothesis is correct.
•Significance is a matter of probability.
•Research Hypothesis: The hypothesis that the variables under
investigation are related in the population- that the observed effect based on
sample data is true in the population.
•(research hypothesis): The population mean of the no-model group is
not equal to the population mean of the model group
•Independent variable did have an effect.
•LOGIC OF THE NULL HYPOTHESIS
•If we can determine that the null hypothesis is incorrect, then we accept the
research hypothesis as correct.
•Acceptance of the research hypothesis means that the independent variable
had an effect on the dependent variable.
•PROBABILITY AND SAMPLING DISTRIBUTIONS
•Probability- The likelihood that a given event (among a specific set of
events) will occur.
We all use probabilities frequently in everyday life.
oExample: the weather forecaster says there is a 10% chance of rain
today; this means that the likelihood of rain is very low.
Probability in statistical inference is used in much the same way.
The probability that an event (in this case, a difference between means in the
sample) will occur if there is no difference in the population.
•PROBABILITY: THE CASE OF ESP
The use of probability in statistical inference can be understood intuitively
from a simple example;
oExample: you test your friend on their ESP (extrasensory perception)
You test your friend by doing 10 trials and of showing them 5
cards with different symbols on each card; you show these cards
twice in a random order in 1 trial
The null hypothesis is that only random error is operating
The research hypothesis is that the number of correct answers
shows more than random or chance guessing
You can reasonably say that that the person will get 1/5 answers
•You can expect small deviations away from the expected 2
answers correct per trial
oHow unlikely does a result have to be before we decide it is significant?
A decision rule is determined prior to collecting the data
oThe probability required for significance is called the alpha level
Most common alpha level probability is used is 0.05
•The outcome is considered significant when there is a 0.05
or less probability of obtaining the results; only 5/100
chances that the results were due to a random error
•You can infer using intuition that getting 7/10 answers vs. 2/10 answers
correct on the ESP experiment is unlikely