# Statistics for Behavioral Sciences (UST) Chpt. 5 & 6

Random Sample

is one in which every member of the population has an equal chance of being selected into the study.;

Convenience Sample

is one that uses participants who are readily available.

Generalizability-also called external validity

refers to researchers'' ability to apply findings from one sample or in one context

replication

refers to the duplication of scientific results ideally in a different context of with a sample that has different characteristics,

Volunteer Sample also called self-Selected Sample

is a special kind of convenience sample in which participants actively choose to participate in a study

Convince Sample

The polling organization acquires a sample in the easiest way possible, for example when you fill out a mail survey or a survey in the mall, or if looking at teenagers might go to high school where readily available

Difference between random selection and random assignment

random selection refers to a is randomly selected.method of creating a sample from a population and random assignment refers to a method we can use once we have a sample whether or not the sample

This is almost never used

random selection

this is used frequently

random assignment

What are the risk of sampling

we might not have a representative sample, and sometimes it is difficult to know. We might draw conclusions about the population that are inaccurate.

Conformation Bias

our usually unintentional tendency to pay attention to evidence that confirms what we already believe and to ignore evidence that would disconfirm our beliefs. closely follow illusory correlations.

Illusory Correlation

the phenomenon of believing one sees an association between variables when no such association exists.

Personal Probability also called Subjective Probability

refers to the likelihood of an event occurring based on an individual's opinion or judgment.

Probability

is the likelihood that a particular outcome will occur out of all possible outcomes.

Expected Relative-Frequency Probability

the likelihood of an event occurring based on the actual outcome of many, many trials, only works in the long run.

Trial (in reference to probability)

refers to each occasion that a given procedure is carried out.

Outcome (in reference to probability)

refers to the result of a trial.

Success (in reference to probability)

refers to the outcome for which we're trying to determine the probability.

Formula for Calculating Probability

Determine the total number of trials, Determine the number of these trials with successful outcomes, Divide the number of successful outcomes by the number of trials.

Descriptive Statistics

allows us to summarize characteristics of the sample

Inferential Statistics also called Hypothesis testing

helps us to determine how likely a given outcome is.

Control Group

is a level of the independent variable that does not receive the treatment of interest in a study. It is designed to march an experimental group in all ways but the experimental manipulation itself.

Experimental Group

is a level of the independent variable that receives the treatment or intervention of interest in an experiment.

Null Hypothesis

is a statement that postulates that here is no difference between populations or that the difference is in a direction opposite from that anticipated by the researcher. considered the boring hypothesis cause nothing happens

Research Hypothesis also called Alternative Hypothesis

is a statement that postulates that there is a difference between populations or sometimes more specifically, that there is a difference in a certain direction, positive or negative. considered the exciting hypothesis.

Wen we make a conclusion at the end of a study, the data lead us to conclude one of two things what are the two things

We decide to reject the null hypothesis or we decide to faul to reject the null hypothesis.

When the data suggest that there IS a mean difference we ....?

Reject the null hypothesis

When the data does not suggest a difference, we ....?

Fail to reject the null hypothesis

We never use the word .....? in reference to formal hypothesis testing

Accept

In formal hypothesis testing language what would we say if the research showed no difference?

we failed to reject the null hypothesis

In formal hypothesis testing language what would we say if the research showed a difference

we reject the null hypothesis

What is a type I error?

occurs when we reject the null hypothesis, but the null hypothesis is correct. like a false positive pregnancy test. Detrimental because people normally take some action because of.

In hypothesis testing what are the 2 types of errors

Type I and Type II

Type II Error

when we fail to reject the null hypothesis but the null hypothesis is false. Like a false negative medical test i.e. false negative on a pregnancy test. causes us to fail to take action

Normal Curve

a specific bell-shaped curve that is unimodal, symmetric and defined mathematically.

What are the 2 critical features of the normal curve

the pattern or errors were symmetric, the left side a mirror image of the right side and the middle of the normal curve represented the best estimate of reality because it averaged the errors.

The shape of the distribution becomes more normal as ? happens

the population or sample size increases

Z Score

is the number of standard deviations a particular score is from the mean.

The process of standardization

converts individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation and percentiles

The Z distribution always has a mean of ? and a deviation of ?

mean is 0 deviation is 1

Steps to figure Z

Subtract the mean of a population from your score then divide by the standard deviation of the population
Z= (X-U0 / O don't forget to watch for negatives so do not make positive

Convert Z score to raw score steps

Multiply the z score by the standard deviation of the population then add the mean of the population to the product.
X= z(O)+U

As long as we know the mean and standard deviation of the population what 2 things can we do?

calculate the raw score from it's z score and calculate the z score from the raw score.

Z distribution

is a normal distribution of standardized scores

Standard Normal Distribution

is a normal distribution of z scores

What 4 things does the standardized z distribution allow us to do

transform raw scores to z scores, transform z scores to raw scores, compare z scores to each other and transform a z score to a percentile.

Describe the process of standardization

we convert individual scores to standardized scores for which we know percentiles.

Central Limit Theorem

demonstrates that a distribution made up of the means of many samples (rather than individual scores) approximates a normal curve, even if the underlying population is not normally distributed

Distribution of Means

is a distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population.

What is the name for the standard deviation of a distribution of means

standard error

Standard Error Formula

Om=O/Square root of sample size (abbreviated by an N)

Distribution Scores

symbol for mean is u, symbol for spread is O name for spread is standard deviation

Distribution Means

Symbol for mean is Um, symbol for spread is Om Name for spread is Standard error

What symbol do you use when calculating the z score based on mean rather than the X we use for individual scores

M

The formula for Z statistic based on mean of population formula

z= (M-Um)/Om

What does Z statistic tell us

how many standard errors a sample mean is from the population mean.

According to central limit theorem a distribution of sample means based on ? or more scores approximates the normal distribution

30

What is the main idea behind the central limit theorem?

It says that a distribution of sample means approaches the shape of the normal curve as sample size increases and that the spread of distribution of sample means gets smaller as the sample size gets larger

What is a distribution of means

is composed of many means that are calculated from all possible samples of a particular size from the same population

The mean of a distribution score is 57 with a standard deviation of 11. Calculate the standard error for a distribution of means based on a sample of 35 people.

Om=O? square root of N or 11/ square root of 35 for an answer of 1.86