unit 5 Flashcards
What is the difference between a parameter and a statistic?
Parameters (𝜃) are used to make conclusions about a population, while statistics (መ𝜃) are used to make conclusions about a sample. Statistics are estimators of parameters.
What is the goal of inferential statistics?
The goal of inferential statistics is to make conclusions about a population based on data from a sample, using probability theory.
What are the three types of hypotheses?
The three types of hypotheses are conceptual, operative, and statistical.
Describe a conceptual hypothesis.
A conceptual hypothesis is a direct statement that is easy to understand.
Describe an operational hypothesis.
An operational hypothesis is quantifiable, measurable, and analyzable, and specifies how variables will be measured.
Describe a statistical hypothesis.
A statistical hypothesis is formulated in terms of statistics or parameters, and is precise and specific.
What is a null hypothesis (H0)?
A null hypothesis (H0) always assumes equality, suggesting no effect, difference, or association. It is the opposite of the alternative hypothesis.
What is an alternative hypothesis (H1)?
An alternative hypothesis (H1) is the opposite of the null hypothesis, suggesting an effect, difference, or association. It is based on the research (operative) hypothesis.
What is a directional hypothesis?
A directional hypothesis predicts a particular direction of difference between populations.
What is a non-directional hypothesis?
A non-directional hypothesis does not predict a particular direction of difference.
How are the null and alternative hypotheses related?
Null and alternative hypotheses are complementary and exclusive; accepting one means rejecting the other.
What is a one-tailed test, and when is it used?
A one-tailed test is used with a directional hypothesis, testing for a difference in a specific direction.
What is a two-tailed test, and when is it used?
A two-tailed test is used with a non-directional hypothesis, testing for a difference in either direction.
What is a p-value?
A p-value is the probability of observing a particular statistic by chance, assuming the null hypothesis (H0) is true.
What does a low p-value suggest?
A low p-value suggests that the probability of the null hypothesis (H0) being true is reduced and indicates statistical significance.
What is the typical significance level (α) in hypothesis testing?
The typical significance level (α) is 0.05, meaning a probability of chance lower than 5% is considered significant.
What does it mean to reject the null hypothesis?
Rejecting the null hypothesis means there is enough evidence to support the alternative hypothesis.
If a study has a p-value of 0.0124, what does that mean in relation to the null hypothesis if the significance level is 0.05?
It means that the null hypothesis is rejected because the p-value is less than 0.05.
What is a Type I error?
A Type I error occurs when the null hypothesis (H0) is true but is rejected. It is a false positive.
What is a Type II error?
A Type II error occurs when the null hypothesis (H0) is false but is accepted. It is a false negative.
What is assumed about scores and statistics in inferential statistics?
It is assumed that scores and statistics follow a certain distribution, often a normal distribution.
What does the central limit theorem state?
The central limit theorem states that if a random variable (X) is normally distributed in the population, and we select infinite samples of size N and calculate their mean, the distribution of sample means will approximate a normal distribution.
What are parametric tests?
Parametric tests make assumptions about the parameters of the population distribution, often assuming the population data are normally distributed.
What are non-parametric tests?
Non-parametric tests are ‘distribution-free’ and can be used for non-normal variables.
What is a confidence interval?
A confidence interval is an estimated range of values (symmetrical with respect to the mean) within which the true population parameter is likely to be found, with a high and known probability.
How is the standard error related to the calculation of a confidence interval?
The standard error of the statistic is used to calculate the maximum sampling error (Emax), which is then used to calculate the upper and lower limits of the confidence interval.
In a one-tailed hypothesis test where the sample mean is 1.5, the population mean is 2, and the standard error is 0.47, what is the z score?
The z-score would be -1.06.
In a two-tailed hypothesis test where the sample mean is 8, the population mean is 9, and the standard error is 0.42, what is the z score?
The z-score would be -2.38.
How do you calculate the maximum sampling error (Emax)?
The maximum sampling error (Emax) is calculated by multiplying the z-score (𝑧𝛼/2) by the standard error of the statistic (Ƹ).
How do you calculate the upper and lower limits of a confidence interval?
The lower limit (LL) is found by subtracting the Emax from the sample statistic, and the upper limit (UL) is found by adding the Emax to the sample statistic.
two-tailed evaluates…
if H1 evaluates whether the mean is different (=/) (-1 and times it by two)
left-tailed evaluates…
if H1 evaluates whether it is less than (<)
right-tailed evaluates…
if H1 evaluates whether it is more than (>) (-1 of z-table)
