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Statistics
it is a science of data, and in statistics it involves summarizing, analyzing, and interpreting the information or numerical info.
is a way of viewing reality as exists around us in a way that we otherwise could not.
Population
set of all individuals or group of people of interest in a particular study
Parameter
- a numerical value that describe a population,
Sample
set of individuals selected from the population that intended to represent the population.
Statistic
- a numerical value that describe a sample
Variable
it is a characteristic that changes or has different values for individuals.
GENERALIZED
Remember (THE RESULTS FROM THE SAMPLE ARE ________ TO THE POPULATION)
Constant
does not vary, it is the same for every individuals.
Values
possible number or category that a score can have.
Score
particular sample’s value on variable.
Data
(plural) - are measurements or observations
Datum
(singular) - single measurement or observation or this what we called score or raw score.
Data set
collection of measurement or observation
Descriptive Statistics
statistical procedures used to summarize, organize, and simplify data.
It gives glance look to the whole data set gathered from the respondents
Frequency Distribution
it is an organized tabulation of the number of individual located in each category on the scales measurement.
Frequency Table
an ordered listing of number of individuals having each of the different values for particular variable
samples
n= for treating ______
Population
N= _______ data
Median
middle score for a set of data arranged in order of magnitude.
Mean (Average)
most often used in continuous data and discrete data. (Denoted by μ)
Mode
- is a value which occurs most often or most frequently occurring observation. (𝐷𝑒𝑛𝑜𝑡𝑒𝑑 𝑏𝑦 𝑀𝑜)
Unimodal
one mode or one peak in the distribution
Bimodal
Bimodal
Multimodal
- three or more peaks in the distribution
Cochran’s Formula
it is use when the population is known (The value should be rounded into hundreds)
Slovin’s Formula
to calculate the sample size necessary to achieve a certain confidence interval when sampling a population.
Proportion
- it measures the fraction of the total group that is associated with each score
Percentage
it expressed as a number out of 100
Multiply the value of proportion to 100
Range
a set of data that is the difference between the highest and the lowest values in the set.
R= = 𝐻𝑖𝑔ℎ𝑒𝑠𝑡 𝑠𝑐𝑜𝑟𝑒 − 𝐿𝑜𝑤𝑒𝑠𝑡 𝑆𝑐𝑜𝑟E
Class Size
- it gives the size of the table
𝑘 = 1 + 3.32𝑙𝑜𝑔(𝑛)
Class Interval
it determine the width of any class in particular distribution
class mark
- this is the value between lower limit and upper limit
Standard Deviation
- is a measure of how dispersed the data is in relation to the mean.
Histogram
Bar like graph of a frequency distribution in which the values are plotted along x-axis and the high of each bar is the frequency of the value(No space ang bars)
Frequency Polygon
continuous line that represents the frequencies of scores within a class interval (it is always based on Histogram)
Column Chart
A data visualization where each category is represented by a rectangle (May space ang mga bars)
Bar Graph
Identical to column charts, but in this chart CATEGORIES are organized vertically on y axis and values are shown in x axis.
Line Graph
(Line plot or line chart)- it is a graph uses a lines to connect individual data points that display quantitative values over a specified time interval. (If our variable is about time this graph is appropriate)
Scatter Plot
uses dots to represent values for two different numeric variables.
Stem and Leaf
is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.
Gaussian Curve
is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a "bell curve”
Karl Friedrich Gauss
He coined the term Gaussian Curve
Abraham de Moivre
Who introduce the first concept of Normal Curve
Skewness
is the degree of asymmetry observed in a probability distribution.
Z-Score
a statistical measurement that describes a value's relationship to the mean of a group of values. ____ is measured in terms of standard deviations from the mean. If a ______ is 0, it indicates that the data point's score is identical to the mean score.
Z-Table
tools used to get exact proportion or probability
𝑧 = 𝑥 −MEAN / SD
Formula for z
𝑆𝐷 = x - mean / z
formula For SD
z x Sd + μ
formula for x
x + sd x z
formula for mean
Kurtosis
a measure of the tailedness of a distribution
Mesokurtic
Medium tail
Platykurtic
Flat tail
Leptokurtic
Thin tail
Inferential Statistics
consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected
T- Test
a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.
Z-test
a statistical test to determine whether two population means are different when the variances are known and the sample size is large. A z-test is a hypothesis test in which the z-statistic follows a normal distribution. A z-statistic, or z-score, is a number representing the result from the z-test.
Z-tests and T-tests
Definition: they are calculations used to test a hypothesis.
Most Useful For: Determining statistically significant differences between two independent sample groups.
Z-test
Used when the population variance is known or when the sample size is larger than 30 with an unknown population variance.
T-test
Used when the sample size is less than 30 and the population variance is unknown
Pearson correlation coefficient
assesses the linear relationship between variables,
Spearman correlation coefficient
evaluates the monotonic relationship
Sampling error
is the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter.
Discrete variable
A discrete variable consists of separate, indivisible categories. No values can exist between two neighboring categories.(Categorical like male/ female, names and more)
Continuous variable
For a continuous variable, there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts. (Decimals )
Nominal, Ordinal, Interval, Ratio
Levels of Measurements
Descriptive Statistics
- One group with one or more separate variables measured for each individual Numerical or category Describing the individual variable
Behavioral Observation
observes and systematically records the behaviour of individual to describe the behaviour.
Frequency
kung ilan
Duration
kung gaano kahaba
Interval
period of time between the events
Naturalistic or non-participant, Participant observation, Contrived or structured
Types of observation
Naturalistic
or non-participant- Observe in a natural setting as unobtrusively as possible
Participant observation
engages in the same activity.
Contrived
or structured - arranged specifically to facilitate the occurrence of specific behaviors.
Open-ended, Restricted, Rating scale
Types of Questions
Open-ended
– Anything you want to answer
Restricted
Multiple choices, or something have a restricted question, have a limitations.
Rating scale
Likert- scale
Case study
case study may involve an intervention or treatment administered by the researcher
CASE HISTORY
Not include any treatment
Correlational Research
One group with two variables measured for each individual (determining whether there is a relationship between the two variables)
Limitation
Demonstrate the existence of relationship No explanation
It does not establish the cause and effect
Predictive research design
Predicting the outcome.
Comparative research design-
comparing two or more groups with one variable.
Experimental Research Design
to answer the cause and effect questions about the relationship between two variables.
Manipulation
something purposefully change by the researcher in the environment
Control
used to prevent outside factors from influencing the study outcome
random selection
equal chance and assignment. Equal chance of being assign in treatment
Control condition or group
does not receive ant treatment instead they received neutral or placebo
Purpose= to provide baseline for comparison group
Experimental condition
or group- do receive the experimental treatment
Quasi-experimental Research
uses some of the rigor and control that exist in experiments;
always contain a flaw prevents from obtaining an absolute cause and effect answer
Pre- test / post-test design
= you will giving before and after treatment and then you will observe if there is any changes of the given treatment or condition
Longitudinal Design
= involved repeted observation of the same variables over short or long period of time. (For years)
Target Population
researcher’s specific interest with the individual share one characteristics.
Accessible Population
can be accessed by the researchers
Representativeness
the characteristics of the sample accurately reflect the char. of the population.
Representative sample
= same characteristics as the population.
Biased sample
different characteristics from population
Selection bias or sampling bias
= are selected in a manner that increases the probability of obtaining a biased sample
Probability sampling
= the entire population is known ( alam mo na dito yung participants mo)