Interpreting Statistics: Statistical Reasoning in Everyday Life Lesson Flashcards
Statistics are important ______ for psychological scientists and are valuable for everyone in helping to reveal insights that _______ ______be apparent to the naked eye
Statistics are important TOOLS for psychological scientists and are valuable for everyone in helping to reveal insights that MIGHT NOT be apparent to the naked eye
To be a well-informed individual today means possessing the ability to apply basic statistical concepts to everyday thinking.
When making a graph make sure to have the Dependent/Reciving Variable on the _ axis and the Independen/Manipulating Variable on the _ axis
When making a graph make sure to have the Dependent/Reciving Variable on the Y axis and the Independen/Manipulating Variable on the X axis
There are _ categories of Research. Descriptive Research does what: just looks at interesting cases and ________it. It doesn’t look at the ______________.
There are 3 categories of Research. Descriptive Research does what: just looks at interesting cases and DESCRIBES it. It doesn’t look at the CORRELATION.
Parts of Descriptive statistics
Measures of Central Tendency (Mean, Median, Mode, and Percentile Rank)
and
Measures of Variability (standard dev & Range)
Descriptive Statistics play a crucial role in ____________ & ___________ data to identify patterns and trends within a set of information
ORGANIZING & SUMMARIZING DATA
Inferential statistics assist in making _________ ________ based on observed differences
Inferential statistics assist in making broader conclusions based on observed differences
Inferential Statsitics ask is this study ____________ _______ , in other words can the findings be applied to the larger population from which the sample was collected.
STASTICLLY SIGNIFICANT
Researchers use statistics to:
organize and assess their collected data, support hypotheses, and draw valid inferences
However, it is also important to recognize that statistics have the potential to be manipulated to ________
DECIEVE
Statistics provide a universal language for structuring, summarizing, and drawing conclusions from gathered information.
By setting up _________ and tallying the _________ of each category, descriptive statistics help us understand the ________ of a particular behavior or event.
By setting up CATEGORIES and tallying the OCCURENCES of each category, descriptive statistics help us understand the FREQUENCY of a particular behavior or event.
Common ways to visualize Descriptive Data:
Histograms(A type of bar graph)
Histograms
A graph that uses rectangles to show the frequency of data items in intervals
Central tendency Definitions
A single reference point that summarizes data & represents a set of scores
Measures of Central Tendency
Mean , Median, Mode & percentile Rank
The mean is calculated by ?
The mean is the _______
summing all the scores and dividing by the total number of scores, giving an average value.
The median is the:
The median is the middle score that divides the data into two halves
the mode is:
the most frequently occurring score in the distribution
Percentile rank is:
the percentage of scores less than a given score
Percentile rank provides insight into:
provides insight into where a particular score stands within the data set.
While measures of central tendency offer valuable insights, it’s essential to consider the impact of ________ ____________
it’s essential to consider the impact of skewed distributions
A lopsided distribution influenced by a few extreme scores affects the _____ greatly
the mean may not accurately reflect the center of the data
Researchers must always be mindful of _____ measure of central tendency they are utilizing and whether any _____ are affecting the results
Researchers must always be mindful of WHICH measure of central tendency they are utilizing and whether any OUTLIERS are affecting the results
Researchers can effectively summarize and interpret data for meaningful analysis by understanding the
MEASURES OF CENTRAL TENDENCY
Measures of Central Tendency indicate where most values in a distribution lie.
Shows how data’s tendency to ____ around a middle value.
Measures of Central Tendency indicate where MOST values in a distribution lie.
Shows how data’s tendency to CLUSTER around a middle value.
Finance
In the field of finance, analysts often use measures of central tendency to understand market trends and make investment decisions. For example, when analyzing stock prices, knowing the mean, median, and mode can help investors determine the average price, the middle point, and the most frequently occurring prices. This information is vital for assessing the stability and potential profitability of investments.
Education
In education, teachers and administrators use central tendency measures to evaluate student performance and set academic standards. By looking at the mean scores on standardized tests, educators can assess the overall performance of a class or school. Understanding the median can help identify middle-performing students, while the mode can highlight areas where students excel or struggle the most.
Healthcare
In healthcare, central tendency measures are essential for analyzing patient data and assessing treatment outcomes. For instance, doctors may use the mean, median, and mode to understand the effectiveness of a particular medication based on patient response rates. Percentile rank can also help identify patients who may require additional medical attention based on their relative health status compared to others.
Marketing
Marketers often rely on central tendency measures to analyze consumer behavior and market trends. By examining the mean, median, and mode of sales data, companies can identify popular products, target specific customer segments, and adjust pricing strategies accordingly. Understanding central tendency helps businesses make informed decisions to optimize their marketing efforts.
Social Sciences
Researchers in the social sciences use central tendency measures to analyze survey data and draw conclusions about human behavior. For example, in a study on income distribution, understanding the median income can provide insights into the typical earnings of a population, while the mode can highlight common salary ranges. Percentile rank can also help identify income disparities and socioeconomic trends within a society.
Normal distribution is often the goal in research and what the researcher ______ to achieve
WANTS
In a normal distribution, the ____,_____, and ____ are all the same and fall at the highest peak of the curve of a bell-shaped polygon
In a normal distribution, the MEAN, MEDIAN, and MODE are all the same and fall at the highest peak of the curve of a bell-shaped polygon
Standardized tests produce a normal distribution and can be explained in more detail by examining variability(A variability is a single number that presents information about the spread of scores in a distribution.).
Measures of variability/________ are ______ & ______ ________
Measures of variability/VARIATION are
RANGE AND STANDARD DEVIATION
Measures of Variation indicates how far apart data is
Range describes
the distance from the highest to the lowest scores on a data set.
Standard Deviation describes how fara data points are from the ______
Standard Deviation describes how fara data points are from the mean
In a Normal Distribution chart the mean, median and mode are all the ____ number
SAME
Normal Distribution chart Percentages:
68%, 95%, 99.7%
Distributions aren’t always Normal, sometimes you can get a ________ Distribution
SKEWED DISTRIBUTION
What causes Skewed Distributions?
Outliers
If there is a one/few high score(s) and majority are lower than it is a ___________ _________ Distribution
POSITIVLEY SKEWED DISTRIBUTION
If there is a one/few low score(s) and majority are higher than it is a ___________ _________ Distribution
NEGATIVLEY SKEWED DISTRIBUTION
How to Solve for Range
It can be achieved by subtracting the smallest number from the highest number
Standard deviation is another measure of _______ & describes the distance of scores around the ___
It measures:
Standard deviation is another measure of VARIANCE & describes the distance of scores around the MEAN
It measures:
How spread out a set of scores is
Standard deviation is the ______ ______ of Variance
Square Root
Low standard dev = Data points are ______ to the mean
CLOSER
High Standard Dev = Data points are ____ from mean
FAR
Label standard deviation (1 - 3) in normal distributions & state the corresponding percentages
In a normal distribution, approximately 68% of the scores are within one standard deviation (SD), 95% are within 2 SD, and 99.7% are within 3 SD from the mean, as illustrated in the image.
Inferential statistics play a crucial role in research by
helping researchers determine if their hypothesis can be supported and their findings can be applied to a larger population.
Researchers seek at least 95% assurance that their hypothesis can be supported, often indicated by a P value of .05 or less. This value serves as the threshold for statistical significance, indicating how likely it is that the obtained results occurred by chance.
In statistics, a p-value (probability value) helps determine the significance of your results in a hypothesis test. It measures the probability of obtaining the observed results, or more extreme results, if the null hypothesis is true.
Key points about the p-value:
Low p-value (typically ≤ 0.05): Indicates that the observed results are unlikely under the null hypothesis, leading researchers to reject the null hypothesis and conclude there may be a statistically significant effect or difference.
High p-value (> 0.05): Suggests that the observed results are consistent with the null hypothesis, meaning there isn’t enough evidence to reject it.
T-Test in Inferential Statistics
In inferential statistics, a t-test is a hypothesis test used to determine if there is a significant difference between the means of two groups. It is commonly used when a small sample size (typically less than 30) is used to compare the means of two groups to see if they are statistically different from each other.
There are different types of t-tests, including:
Independent Samples T-Test: Used when comparing the means of two independent groups.
Paired Samples T-Test: Used when comparing the means of two related groups.
One-Sample T-Test: Used when comparing the mean of a single group to a known value.
The t-test calculates a t-statistic, then compares it to a critical value from a t-distribution to determine if the difference between the groups’ means is statistically significant. It helps researchers make inferences about the population based on sample data.
