Psych Stats Final

An entire group of individuals

group of individuals selected to represent the population as usually populations are too large to examine the entire group

parameter (the p’s go together)

statistic (the s’s go together)

the scale chosen determines the types of questions that can be answered with the data: nominal, ordinal, interval, and ration

an unordered set of categories identified by name only

an ordered set of categories, tells you the direction of difference between two individuals

an ordered series of equal sized categories, identify the direction and magnitude of a difference, zero point is located arbitrarily

an interval scale where a value of zero indicates none of the variable, identify the direction and magnitude of differences

Nominal, ordinal, interval, ratio

Ordinal, interval, ratio

Interval, ratio

Ratio

determine the strength and direction of the relationship between two variable

uses observations of the two variables as they exist naturally

Correlation does not equal causation

examine the relationship between 2 (or more) variables by changing one variable and observing the effects on the other variable

Only studies that identify causation

a condition or event manipulated by experimenter (I decide)

an aspect of behavior thought to be affected by the independent variable (Depends on what I decide)

similar to experiments because they also compare groups of scores, do not use a manipulated variable to differentiate groups, the IV is a pre existing participant variable or a time variable

Number of individuals in a data set for a population

Number of individuals in a data set for a sample

each score is divided into a stem consisting of the first digit(s) and leaf consisting of the final digit

Go through the list of scores one at a time and write the leaf for each score besides its stem

the most frequently occurring score or class interval in the distribution

nominal, ordinal, interval, or ratio

there can be multiple

divides the scores so that 50% have values equal to or less than the median; if sores are listed smallest to largest, the median is the midpoint of the list

ordinal, interval, or ratio

no the medians tends to stay in the “center” of the distribution regardless of extreme scores

calculated by computing the sum or total for the entire set of scores and dividing the sum by the number of scores; the balance point of the distribution

ordinal, interval, or ratio

a few extreme scores, or is very skewed; humped distribution and the mean score might actually represent no data value in the distribution

mean and median will always be equal

mean, mode, and median will always be equal

will be located at the peak on one side (closer to the steep slope)

will be displaced toward the tail

will be located between the mean and the mode

scores pile up on one side of the distribution

scores tend to pile up on the left side of the distribution with the tail pointing right.

scores tend to pile up on the right side with the tail pointing left

standard deviation for a population

standard deviation for a sample

the sum of the squared deviation values (value minus mean)

“average” the squared deviations from the mean

1. Determine each scores deviation (dist from mean)

2. Square the deviations

3. Sum them, and average the squared deviations

   For population divide by N, for sample divide by n-1

square root of the variance

Standard deviation

The average distance between each data point and the mean of a dataset

• the dispersion or variability of the data

the sum of squares is divided by df (n-1) instead of just the total number of observations (N)

degrees of freedom (n-1); accounts for the fact that sample variance will typically underestimate population variance

tell us how far away the point is from the mean as a proportion of standard deviation

value is above the mean

value is below the mean

is the mean

can compare distributions with different scales

The likelihood of an event occurring

= specified outcome / total outcomes

12:52 or 3:13

0.23

23.08%

Used to calculate the likelihood of obtaining a specific sample from a given population

If the probability of getting a specific the sample is low, we can say that the sample probably came from some other population

A statistical technique used to select a subset of individuals or items from a larger population

each member of the population has an equal chance of being chose

ensures that the sample is representative of the population and reduces bias.

Every individual has an equal chance of being chosen

Ensuring unbiased representation and increases the generalizability of the findings

• Draw a vertical line at the data point

• The line divides the distribution into 2 sections: the body and the tail

• The exact location of the line can be specified by a z-score

• Look at z-score table to see the proportion in body and tail.

First, transform the score into a z-score

Then look up the z-score in the table and read across the row to find the appropriate probability

First, look up the proportion in the table and read across the row to find the appropriate z-score

Then transform the z-score into a x-value

-+1.96

A probability distribution that is symmetric and bell-shaped. It is characterized by its mean (μ) and standard deviation (σ).

• The majority of the data falls near the mean, with fewer data points further away from the mean.

• The shape of the distribution is determined by the mean and standard deviation.

• The area under the curve represents the probability of observing a particular value or range of values.

The difference between a sample statistic and the true population parameter it represents.

It occurs due to the inherent variability in the process of selecting a sample from a larger population.

Quantified using measures such as margin of error or standard error.

The bigger the sigma the wider the distribution

the population mean

• The shape of the distribution of sample means is typically normal

• Distribution of sample means approaches a normal distribution as n approaches infinity

the larger the sample size the Smaller the variability

• the population the samples are obtained from is normal

• the sample size is n=30 or more

The observed findings are due to random chance (there does not appear to be a real effect)

Predicts that the independent variable had no effect on the dependent variable

The observed findings cannot be explained by sampling error (there does appear to be a real effect)

Predicts that the independent variable did have an effect on the dependent variable

If the test statistic results are in the critical region, we conclude the difference is significant (an effect exists)

If the test statistic is not in the critical region, conclude that the difference is not significant (any difference is just due to chance)

Establishes a criterion, or "cut-off", for deciding if the null hypothesis is correct.

Typically α = .05 (rarely α = .10 or α = .01)

The smaller the alpha level the less likely to reject the null (smaller critical region)

The larger the alpha level the more likely to reject the null (larger critical region)

Occur when the sample data indicate an effect when no effect actually exists.

• Rejecting the null hypothesis when the null is true.

• Caused by unusual, unrepresentative samples, falling in the critical region without any true effect.

• Hypothesis tests are structured to make Type I errors unlikely.

Occur when the hypothesis test does not indicate an effect but in reality an effect does exist.

• We fail to reject the null hypothesis even though it was actually false.

• More likely with a small treatment effect or poor study design (sample size too small).

The probability of obtaining an effect at least as extreme as the one in your sample data, assuming the truth of the null hypothesis

Used when performing hypothesis tests; the statistical significance is checked by seeing if our test scores (ex z-score) indicate a p-value of less than our α

Probably about 20-50% depending on context

Assuming the null is true, you’d obtain the observed difference or more in 5% of studies due to random sampling error.

Measures of the absolute magnitude of an effect, independent of sample size

• Standardized effect size

• Like a z-test, measures mean difference in terms of the standard deviation

Because effect size provides a measure of the practical significance of the results.

• Hypothesis tests determine if there is a statistically significant difference, and effect size quantifies the magnitude of the difference.

Sample Size: Effect size is independent of sample size

Standard Deviation: Effect size is inversely related to the standard deviation

The probability that the test will reject the null hypothesis when there is actually an effect

It represents the probability of detecting a true effect or relationship between variables.

A higher power indicates a greater likelihood of correctly rejecting the null hypothesis and avoiding a Type II error (false negative).

A well-powered test increases the confidence in the results and enhances the reliability of scientific conclusions.

• effect size (larger effects are easier to find)

• sample size (larger samples make it easier to find effects)

• alpha level (larger alpha level makes it easier to find effects

• non-directional vs directional hypothesis (directional tests make it easier to find effects)

"estimated z-test.“

• Estimated because we are using the sample standard deviation to estimate the unknown population standard deviation.

Allows researchers to use sample data to test hypotheses about the difference between a sample mean and a population mean.

The t statistic does not require knowledge of the population standard deviation (σ)

Can be used for a completely unknown population (both μ and σ are unknown)

• All that required is a sample and a reasonable hypothesis about μ

1. One-sample t-test (when you don’t know μ or σ, but can approximate μ)

2. Independent Samples or Independent Measures t-test (when you don’t know μ or σ, and cannot approximate μ, and are studying 2 sample)

3. Dependent Samples or Repeated Measures t-test (when you don’t know μ or σ, and cannot approximate μ, and are studying 1 sample)

The hypothesis test with a t statistic follows the same four-step procedure that was used with z-tests:

1. State the hypotheses and select a value for α. (Note: The null always states a value for μ.)

2. Locate the critical region. (Note: You must find the value for df and use the t distribution table.)

3. Calculate the test statistic.

4. Make a decision. (Either "reject" or "fail to reject" the null hypothesis.)

Need to calculate the degrees of freedom

• df = n – 1 = 25 – 1 = 24

Then we go to the t distribution table.

• Since we are using a non-directional hypothesis the test is two-tailed

• Since our alpha level is .05 go to column with .05 in two tails

• Go to the row corresponding to our df.

• Take note of Critical Region

• With large samples, the t value will be very similar to a z-test.

• With small samples, however, the t-value will provide a relatively poor estimate of z.

Sample variance affects the t-test by influencing the calculation of the t-statistic

A larger sample variance leads to a larger standard error and a smaller t-statistic, making it less likely to reject the null hypothesis

A smaller sample variance leads to a smaller standard error and a larger t-statistic, making it more likely to reject the null hypothesis.

For t-test

Percentage of Variance Accounted for by the IV

• Scores differ across individuals for many reasons.

• By measuring the amount of variability that can be attributed to the IV, we obtain a new measure of effect size