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 sample data.
•In addition to describing sample data, we want to make statements about populations.
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
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%
•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 values.
•Equivalence of groups is achieved by experimentally controlling all other variables or by
•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. (usually valid)
•It is also true that the difference between any two groups will almost never be zero.
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
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
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 right
•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
oThe probabilities shown were derived from a probability distribution called the
oAll statistical significance decisions are based on probability distributions such as
•Called sampling distributions
•The sampling distributions are based on the null hypothesis
•All statistical tests rely on sampling distributions to determine the probability that the
results are consistent with the null hypothesis
oWhen the results are very unlikely according to the null hypothesis expectations
the null hypothesis is rejected
•The total number of observations on determinations of statistical significance
•In the ESP example; let’s say you tested your friend on 100 trials instead of 10 and
observed 30 correct answers
o30/100 is less likely then 3/10
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 sample data. Example: people in one state might tell you that 57% prefer the democratic candidate and that. Reflects any true differencein the population means, plus. 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. this is what is meant by statistical significance. Independent variable did have an effect: logic of the null hypothesis. we all use probabilities frequently in everyday life: example: the weather forecaster says there is a 10% chance of rain today; this means that the likelihood of rain is very low.