stats: visual display and normal curve (z- score)

*visual display *normal curve - z-score *hypothesis testing - anova and t- test

What is the mean of the z distribution?

The mean of the z distribution is always 0.

What is the standard deviation of the z distribution?

- The standard deviation of the z distribution is always 1.

4. What does the normal curve allow us to convert scores to?

It allows us to convert scores to percentiles.

7. What do we convert raw scores to for more specific comparisons?

We convert raw scores to z scores.

What type of distribution is the z distribution?

It is a normal distribution of standardized scores.

What is the standard normal distribution?

It is a normal distribution of z scores.

What can z scores be used for?

it can be used for comparing scores from different distributions.

What can z scores be transformed into?

it is using the normal curve to determine percentages under the curve.

What can we convert using the normal curve and standardization?

We can convert raw scores to z scores and z scores to percentiles.

Why are z scores helpful?

it give us a sense of where a score falls in relation to the mean and standard deviation

of its population.

What does the z distribution form?

it forms a normal curve with a unimodal, symmetric shape.

What is the purpose of standardization?

allows us to determine the percentage of any area under the normal curve.

How can we compare two z scores?

by standardizing them based on their respective distributions.

Why is there a need to use standard scores in interpreting data?

it allows for direct comparisons between scores on different measures.

What did De Moivre's equation describe?

• described the normal curve, a bell-shaped curve that is unimodal,

• symmetric, and defined mathematically.

What were two critical features of the normal curve observed by early astronomers?

• The normal curve was symmetric and errors clustered tightly around the middle, resembling a

• bell-shaped pattern.

What is the purpose of standardization?

• converts individual scores to standardized scores, allowing for meaningful

• comparisons between distributions.

What are the characteristics of a z score?

The mean of a z score is always 0 and the standard deviation is always 1, irrespective of the ,original distribution.

What does the central limit theorem allow us to do?

allows for comparisons between means in addition to scores.

Abraham DeMoivre

the person created the normal curve equation

z- score

also allows us to compare things taht are not on the same scale as long as they are normally distributed

Normal Distribution

• is a density curve

• total area of 1 or 100%

• any type of ________ with any value of mean and SD can be transform into the standard normal distribution / or z -score

we can determine the percentage of any area under normal curve through ____?

standardization

As z distribution forms a ________ with ______ and _______

normal curve with unimodal and symmetric shape

What does the z-scores gives us? 3 answers

1. gives us sense of where score falls in the relation to the mean

2. allows us to compare scores from different distribution

3. can be transformed into percentiles

Central Limit Theorem

It refers to how a distribution of sample means is a

more normal distribution than a distribution of

scores, even when the population distribution is not

normal.

two important principles of the Central Limit Theorem?

1. Repeated sampling approximates a normal curve, even when the original population is not normally distributed,

2. a distribution of means is less

   variable than a distribution of individual scores.

distribution of means?

• distribution composed of many means that

are calculated from all possible samples of a given

size, all taken from the same population.

outcome of a distribution of means?

It is more consistently produces a normal distribution

(although with less variance) even when the

population distribution is not normal.

What does repeated sampling of means produce?

It produces a normal distribution even when the original distribution of scores is not normal.

What is the distribution of means?

It is more tightly clustered than a distribution of

scores.

What would happen if the population used to create

the distribution of means was larger?

More values would be plotted in the distribution of

means.

or ma modako ang spread

central limit theorem?

It is a ________ that requires a distribution comprised

of many sample means to produce an

approximately normal curve.

What is the standard deviation of the distribution of

means?

The distribution of means needs its own standard

deviation, which is smaller than the one used for the

distribution of individual scores.

Why does the distribution of means need its own

standard deviation?

Because the distribution of means is less variable

than the distribution of scores.

What type of curve is produced when means are

repeatedly sampled from an extremely skewed

population distribution?

A normal curve is produced.

What is the formula for calculating the standard

error?

The standard error is the standard deviation of the

population divided by the square root of the sample

size, N.

How does the distribution of means approximate the

normal curve?

The distribution of means will approximate the normal curve if the samples are composed of atleast 30 scores.

What is the purpose of using the central limit

theorem to make comparisons with z scores?

The purpose is to standardize raw scores based on

the population.

What are z scores?

Z scores are a standardized version of raw scores

based on the population.

What does the z statistic represent?

tells us how many standard errors a

sample mean is from the population mean.

How can z scores be used to compare different samples?

can be used to compare different samples by standardizing the means of the samples and comparing the resulting z scores.

What is the purpose of using a z-statistic in

inferential statistics?

To determine how extreme the mean of a sample is

in terms of a percentage.

What is the usefulness of combining a distribution of means and a z-statistic?

It prepares us for inferential statistics and hypothesis testing.

What is the purpose of hypothesis testing in

statistics?

To draw conclusions about the data collected to test a hypothesis.

What are the three different ways to identify the

same point beneath the normal curve in hypothesis

testing?

Raw score, z score, and percentile ranking.

The tool that allows us to transition from one

way of identifying a point to another in hypothesis

testing?

The z table.

Why is the ability to convert individual z scores to

percentile ranks important in hypothesis testing?

It allows for a better understanding of the

significance of the data.

What percentage of scores fall within one z score of

the mean in a normal distribution?

About 68% of scores fall within one z score of the

mean in a normal distribution.

purpose of the z table in hypothesis

testing?

• used to convert raw scores to z statistics and determine percentages associated with a given z score or raw score in hypothesis testing.

• To determine percentages and z-statistics for

  distributions of scores or means.

What are the assumptions that should be met

before conducting a hypothesis test?

1. The dependent variable should be on a scale measure,

2. the data should be from a randomly selected sample

3. the population distribution should be normal or there should be at least 30 scores in the sample.

What is the difference between parametric and

nonparametric tests?

Parametric tests require assumptions, whereas

non-parametric tests do not.

What are the three requirements for data to be used

in a robust hypothesis test?

1. the data should be from a randomly selecteda smple,

2. the sample size should be at least 30,

3. the population distribution should be normal or approximately normal.

What are the six steps for hypothesis testing?

1. Determine the populations, comparison distribution, appropriate hypothesis test, and assumptions.

2. State the null and research hypotheses.

3. Determine the characteristics of the comparison distribution used to calculate the test statistic.

4. Determine the critical values or cutoffs based on a p level / alpha of 0.05.

5. Calculate the test statistic.

6. Make a decision and interpret the results.

What is a robust hypothesis test?

is one that produces valid results even when all assumptions are not met.

What is the significance level typically used in

hypothesis testing?

The significance level typically used in hypothesis

testing is a p level of 0.05.

What is a two-tailed test?

in which the research hypothesis does not indicate a direction of the mean difference or change in the dependent variable, but merely indicates that there will be a mean difference.

What is a z-test?

it is conducted in the rare cases in which we

have one sample and we know both the mean and

the standard deviation of the population.

What is a critical value?

it is a test statistic value beyond which

we reject the null hypothesis; often called a cutoff.

What does the critical region refer to?

refers to the area in the most

extreme 5% (2.5% in each tail) of the comparison

distribution.

What is the critical region in hypothesis testing?

The area in the tails of the comparison distribution

in which we reject the null hypothesis if our test

statistic falls there.

What is the probability used to determine the critical

values in hypothesis testing?

p-value or alpha

What happens if the test statistic is not beyond the

cutoffs in hypothesis testing?

We fail to reject the null hypothesis, meaning that

we can only conclude that there is no evidence from

this study to support the research hypothesis.

What does it mean if the test statistic falls between

the critical values in hypothesis testing?

We fail to reject the null hypothesis and conclude

that there is no evidence from this study to support

the research hypothesis.

What is the definition of "statistical analysis"?

It refers to the process of collecting, analyzing, and

interpreting data to make informed decisions.

 7 types of MISLEADING GRAPHS

1. FALSE FACE VALIDITY LIE -  looks accurate but not when dig depper

2. BIASED SCALE LIE  -    slants information in a particular way

3. SNEAKY SAMPLE LIE  - preselecting participants 

4. INTERPOLATION LIE  - assumes 2 data points follow the same pattern 

5. EXTRAPOLATION LIE - assuming that a pattern will continue indefinitely. / Goes beyond 

6. INACCURATE VALUES LIE - distorting

7. OUTRIGHT LIE - making up data·

common types of graphs

1. scatter plot - relations of  two variables 

2. line graph - time plot series 

3. bar graph - iv: categorical, dv: numerical ; pareto chart - x axis are ordered highest on left and low on right 

4. steam-and-leaf plot - displays all the data points of a variable

5. pictorial graph - pictures 

6. pie chart

7. pictorial graph

• Types of bar graph 

1. Histogram 

2. Frequency polygon - a dot is placed at the frequency for each value

Chart Junk

any unnecessary information or feature in a graph that detracts from a viewer’s ability to understand the data

features of chart junk

• moire vibrations

• grids

• ducks

moire vibrations

patterns that computers provide as options to fill in bars

grids

• type of chart junk that has a background pattern, almost like graph paper, on which the data representations, such as bars